STRENGTH
STRUCTURE PRENTICE-HALL GEOLOGY SERIES Edited by N orman E. A. H inds Strength and Structure of the Earth, by Reginald Aldworth Daly Geophysical E xploration, by C. A. Heiland Sedimentation, by Gustavus E. Anderson STRENGTH AND STRUCTURE OF THE EARTH
By REGINALD ALDWORTH DALY STURCIS HOOPER PROFESSOR OF GEOLOGY HARVARD UNIVERSITY
N ew Y o r k : 1940 PRENTICE-HALL, INC. Copyright, 1940, by PRENTICE-HALL, INC. 70 Fifth Avenue, N ew York ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY MIMEOGRAPH OR ANY OTHER MEANS, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHERS,
PRINTED IN THE UNITED STATES OF AMERICA CONTENTS
CHAPTER PAGE 1. Introductory...... 1 . The Problem...... 1 Vocabulary...... 5 Discontinuities in the Earth...... 16 Calculated Internal Densities...... 21 Figure of the Earth; Geoid, Ellipsoid, Spheroid. . 24 2. D evelopment of the Idea oe Isostasy...... 36 Bouguer to Petit...... 36 Pratt...... 38 Airy...... 42 Hall...... 50 Jamieson...... 50 Dutton...... 51 Gilbert...... 53 Helmert; Schweydar...... 54 Suggestions Regarding Isostatic Compensation.. . 56 3. Testing Isostasy with the Plumb-Line...... 65 Deflections of the Vertical...... 65 Hayford’s First Investigation...... 67 Topographic Deflections...... 70 Construction of the Geoid...... 78 Recognition of Isostasy...... 81 Effect of Isostatic Compensation on the Direc tion of the Vertical...... 87 Statistical Tests of Conclusions...... 94 Degree of Isostatic Compensation...... 99 VI Contents
CHAPTER PAGE 3. Testing Isostasy with the Plumb-Line (Cont.) Amended Ellipsoid of Reference...... 102 Hayford’s Second Investigation...... 102 Conclusions Regarding the Dimensions of Uncom pensated Loads...... 104 4. Measurement oe Gravity; Comparison oe Intensities...... 106 Gravitation...... 106 Relation of Gravity to Latitude...... 109 Measurement of Gravity...... I ll Reduction of Values of Gravity...... 114 Free-air Reduction...... 114 Bouguer Reduction...... 116 Isostatic Reductions...... 120 Indirect Reduction...... 126 Clearing-house for Systematic Record of Anom alies...... 129 5. Gravimetric Tests oe Isostasy in the United States, by Hayford and B owie...... 131 Introduction...... 131 Assumed Conditions for Isostatic Compensation.. 132 Theoretical Gravity at a Station...... 139 Correction for Elevation...... 139 Correction for the Effects of Topography and Compensation...... 140 Specimen Isostatic Anomalies...... 149 Comparison with the Corresponding Free-air and Bouguer Anomalies...... 149 Local Versus Regional Compensation...... 152 Relation of Anomaly to Varying Depth of Com pensation...... 154 Anomalies in Terms of Masses...... 154 General Conclusions...... 156 6. Later Gravimetric Tests oe Isostasy in N orth America...... 159 Bowie Report of 1912...... 159 Bowie Report of 1917...... 161 Contents vii
CHAPTER PAGE 6. Later Gravimetric Tests oe Isostasy in N orth America (Cont.) Bowie Report of 1924...... 174 United States Values of Gravity Reported Since 1924...... 182 Putnam’s Discussion of United States Data...... 184 Gilbert’s Estimate of Uncompensated Loads...... 187 Heiskancn on Gravity in the United States...... 187 Gravity in Canada...... 190 Concluding Remarks...... 191 7. Testing Isostasy in Europe...... 196 Introduction...... 196 Gravity in Alps and Apennines...... 197 Heiskanen’s Studies...... 205 Caucasus...... 205 Norway...... 208 Gravity in Finland...... 210 Gravity Measurements in Cyprus...... 211 Additional European Data...... 213 Review and Forecast...... 215 8. Testing Isostasy in Africa and Asia...... 218 Earlier Work in East Africa...... 218 Bullard on Gravity in East Africa...... 219 Gravity in Siberia...... 224 Conditions in India...... 224 The Geoid in India...... 225 Gravity Anomalies in India...... 236 Observations in Turkestan...... 247 Gravity Anomalies in Japan...... 248 Some Leading Results...... 250 9. Testing Isostasy at Se a ...... 252 Introduction...... 252 Observations of Hansen, Schiotz, and Hecker.. . . 253 Measurement of Gravity at Sea, by Vening Meinesz...... 256 Mean Gravity Anomalies Over the Open Ocean 259 Gravity Anomalies Over Mediterranean Seas. . 264 Strip of Negative Anomalies, East Indies...... 269 viii Contents
CHAPTER PAGE 9. Testing Isostasy at Sea (Cont.) Negative Strip of the West Indies...... 285 Anomalies Over Ocean Deeps Facing Mountain- arcs...... 290 Gravity Profiles off Shores...... 294 Gravity Anomalies in the Vicinity of Volcanic Islands...... 298 Gravity Anomalies at Stations Near Great Deltas 303 Conclusions...... 305 10. N ature’s Experiments with Icecaps...... 309 Introduction...... 309 Jamieson Hypothesis...... 310 Warping of Fennoscandia, Past and Present...... 312 Objections to Jamieson’s Isostatic Hypothesis.... 316 Recoil of the Glaciated Tract of Northeastern North America...... 326 Nansen’s Evidence from the Strandflat...... 330 Summary...... 334 11. Retrospect...... 337 Introduction...... 337 Meaning of the Word “Isostasy”...... 338 Proofs of Close Approach of the Earth to Ideal Isostasy...... 342 Relation of Gravity Anomaly to Spheroid of Ref erence ...... 344 Need of Great Extension of the Gravitational Survey...... 345 Effect of Errors of Mensuration and Computation 348 Effect of Changing the Assumed Type of Isostatic Compensation...... 349 Effect of Changing the Assumed Depth of Com pensation...... 350 Effect of Local Abnormalities of Density of Rock 351 How Permanent are Areas of One-sign Anomaly? 351 12. Strength of the Earth-Shells...... 353 Introduction...... 353 Stresses Caused by Departures from Isostasy. . . . 355 Contents ix
CHAPTER PACE 12. Strength of the Earth-Shells (Cont.) Dimensions of Stable Areas of One-sign Anomaly 361 Anomaly Areas in the United States...... 362 Mechanical Conditions in Peninsular India. ... 364 Anomaly Field Along the Pacific Coast of North America...... 369 Anomaly Field of the Eastern Atlantic and Ad jacent Land...... 371 Anomaly Field of the Western Pacific...... 373 Summary...... 373 Anomaly Fields of the Mediterranean Seas. ... 373 Anomaly Fields of the Open-ocean “Deeps”. . . 376 Anomaly Fields Surrounding Volcanic Islands.. 379 Comparison of Loads on Continental and Oceanic Sectors; Strength of the Lithosphere...... 380 Experiments on the Relation of High Confining Pressure to the Strength of Rock...... 384 The Unstable Glaciated Tracts...... 385 Comparison of Conditions in India and Fenno- scandia...... 390 Horizontal Variation of Thickness of the Litho sphere ...... 393 Strength of the Lithosphere at Earlier Geological Epochs...... 396 The Asthenosphere and Theories of Diastrophism and Petrogenesis...... 398 The Asthenosphere and Deep-focus Earthquakes. 400 The Asthenosphere and Warped Peneplains...... 407 Strength of the Mesospheric Shell...... 408 Conclusions...... 410 Index 419 STRENGTH AND STRUCTURE OF THE EARTH 1 INTRODUCTORY
THE PROBLEM Structural geology records colossal work done by natural forces on the visible and invisible rocks of every continent. The energy expended in this work has been chiefly of two kinds—solar and terrestrial. Geologists of the nineteenth century paid particular attention to the part played by solar radiation in governing the dynamical history of the outer earth. A leading project of the twentieth century is to learn how the conditions of the planet’s deep interior have also controlled the same history. Already some of the necessary data have been secured.* The earth contains a spheroidal core, which, with a radius of nearly 3,500 kilometers and an average density of about 11, is regarded as essentially metallic iron. A number of seismologists suspect this iron to be fluid and devoid of strength. The rest of the planet, beneath ocean and at mosphere, reacts like a solid to the stresses set up by the passage of earthquake waves, and may be distinguished as a whole by the name “mantle.” According to leading geo physicists, the mantle has a mean density approaching 4.5, a thickness of about 2,900 kilometers, and a composition dominated by silicate material. At least the upper part of * A recent summary is given in “Internal Constitution of the Earth,” a volume written by a number of specialists, including its editor, B. Gutenberg. The book, volume 7 of a series on Physics of the Earth, sponsored by the National Research Council at Washington, was published in New York (1939). 1 2 Introductory the mantle has a shelled character, signalized by more or less sharp “discontinuities” in its substance. The seismol ogists have determined approximately the volume compres sibility and the rigidity of mantle-shells and core. Rigidity, or elasticity of figure, is the “instantaneous” resistance of a substance to deformation by a shearing stress. The word “rigidity” is also used as a synonym of “modulus of rigidity,” a quantity equal to the internal tangential stress divided by the amount of shear. The seismically-effective rigidity of each earth-shell is high, generally exceeding that of steel, but the high values have meaning only when con sidered in relation to the small, periodic stresses of elastic waves. For large stresses of long duration the rigidity of a shell may be small. We shall later note ideas of the present day regarding the number and location of the discontinuities. An associated problem of great significance is also under active investigation: that of the location of strength in the earth, a property entirely different from rigidity, strength representing, not the “instantaneous” but the enduring, permanent resistance to a shearing stress with a limiting value. The physical geologist needs to learn all he can about the amount and distribution of the strength, and es pecially to know how the property changes quantitatively from one layer of the mantle to another layer. One relevant fact seems already assured: in spite of the high pressure inside the earth, the strength of its material, unlike the seismically-effective rigidity, begins to diminish at a depth which is a small fraction of the planetary radius. The decrease is rapid, so that the strength may be nearly or quite zero at a level between 60 and 100 kilometers below the surface. There is some reason to think, however, that the strength begins to increase again at a level a few scores or hundreds of kilometers still deeper, to remain consider able until the iron core is approached. Introductory 3 The problem is fundamental. Discovery of the location and degrees of strength in the globe would help us to fix in ternal temperatures and to understand the earth’s shape, the development of mountain chains, the origin of conti nents, floodings and recessions of the sea, igneous action, and metamorphism. The distribution of the strength is the complex and challenging theme of this book. The study must begin with the facts of the surface. The outer layers of the earth form a palimpsest, from which, bit by bit, the record of great events of more than a thousand million years is being deciphered. In general the changes have been orderly, not catastrophic. Since geological time began, the earth has been rugged. The existing topography is an inheritance from a chain of infinitely varied, slow re modelings, but the relief of the surface has always depended on the strength of the superficial rocks and their underground continuations. The structural complexity of the earth’s skin is the result of unbalanced pressures in that skin, and the propagation of the pressures has also depended on the strength of rock, superficial and underground. The hori zontal displacement of rock masses and the vertical displace ment of molten rocks, magmas, become more intelligible if a relatively thin, superficial shell of the earth overlies a much weaker layer. Although the existence of the lower, more plastic layer is indicated by a variety of observations, there is no consensus as to the degree of the plasticity. This re sidual question is so vital to physical geology that it deserves detailed consideration. The present book attempts to sum marize the facts and deductions bearing on the plastic layer and its geometrical relations to the overlying and underlying shells. Attention will be centered on the response of terres trial matter to the force of gravity, itself a combination of gravitational and rotational forces. Cosmical, chemical, magnetic, and electrical forces are here of subordinate interest. 4 Introductory Specifically, then, we are to be concerned with what now appears to be the one and only reliable method of attack on the problem of strength: we shall note in some detail how geophysicists correlate the earth’s relief with gravity as measured on its surface, and then observe how that correla tion can be made to tell how strength is distributed in depth. More technically expressed, we are to study the problem of isostasy, and then to study the meaning of some isostatic adjustments now in progress. The subject has been discussed by Barrell and Jeffreys, but, when their results were published, neither of these pio neers had access to some recently discovered and exception ally vital facts. And there is a second reason for still an other book on modern methods of diagnosing terrestrial strength. The slightest acquaintance with the subject makes one realize how scattered and hard to find in even a great library are the “books of original entry,” that is, the technical works recording field observations on the intensity and direction of the force of gravity or embodying discus sions of those observations. The author’s experience with graduate students has suggested the advisability of compil ing under one cover the essential arguments now being used in connecting the earth’s field of gravity with its field of stress. The collection of vital data has been made easier by the generosity of many leading authorities who have presented copies of their publications. For this help special thanks are due to the Directors of the United States Coast and Geodetic Survey, the Canadian Dominion Observatory at Ottawa, the Survey of India, the Finnish Geodetic Institute, and the Baltic Geodetic Commission; and to individuals— W. Bowie, G. Cassinis, E. A. Glennie, B. Gutenberg, W. Heiskanen, H. Jeffreys, K. Jung, W. D. Lambert, M. Matu- yama, M. Sauramo, F. A. Vening Meinesz, and others. Discussion of difficult problems involving the mechanical Introductory 5 properties of the earth-shells has been particularly facilitated by the publications and advice of the workers in the Harvard laboratories devoted to physics at high pressure, to experi mental geology, and to seismology. Among these investi gators special gratitude is felt toward F. Birch, P. W. Bridg man, E. B. Dane, D. T. Griggs, and L. D. Leet, along with D. Bancroft, H. Clark, R. B. Dow, J. M. Ide, R. R. Law, and W. A. Zisman. However, none of these is to be held responsible for the arguments presented in the text. The author has much pleasure in acknowledging the care with which E. A. Schmitz drafted the illustrations, and, also par ticularly, the courtesy of the Director of the Survey of India in granting permission to copy the maps and sections repre sented by Figures 44-51 inclusive. VOCABULARY For clear understanding it is well to canvass the meaning of the word “strength,” the meanings of other technicalities without which that term can not be defined, and the mean ings of still other expressions needed during an analysis of the general problem before us. The list of such terms in cludes strain, stress, principal stress, stress-difference, funda mental strength, elasticoviscosity, solid, isostasy, isostatic com pensation, isostatic adjustment, lithosphere, asthenosphere, crust, sial, and sima. Strain. The technical term “strain” was brought into mechanics by Rankine, whose classical writing of 1855 con tained the following sentence: “In this paper the word strain will be used to denote the change of volume and figure con stituting the deviation of a molecule of a solid from that condition which it preserves when free from the action of external forces.” 1 Thomson and Tait suggested a purely kinematical definition, so that it should cover deformations of fluid masses as well as of solid bodies. However, this idea has not been accepted, and in general “strain” is defined as 6 Introductory in the Century Dictionary; it is “a definite change in the shape or size of a solid body, setting up an elastic resistance, or stress, or exceeding the limit of elasticity.” Stress. The word “stress” also owes its original, tech nical definition to Rankine: The word stress will be used to denote the force or combination of forces, which such a molecule [of a solid] exerts in tending to recover its free condition, and which, for a state of equilibrium, is equal and opposite to the combination of forces applied to it. Present usage seems to be well defined by J. A. Ewing, writ ing on the Strength of Materials in the eleventh edition of the “Encyclopaedia Britannica” (reprinted by permission): Stress is the mutual action between two bodies, or between two parts of a body, whereby each of the two exerts a force upon the other. . . . In a solid body which is in a state of stress the di rection of the stress at an imaginary surface of division may be normal, oblique, or tangential to the surface. When oblique it is conveniently treated as consisting of a normal and a tangential component. Normal stress may be either push (compressive stress) or pull (tensile stress). Stress which is tangential to the surface is called shearing stress. Oblique stress may be regarded as so much push or pull along with so much shearing stress. The amount of stress per unit of surface is called the intensity of stress . . . usually expressed in tons weight per square inch, pounds weight per square inch, or kilogrammes weight per square milli metre or per square centimetre. . . . It may be shown that any state of stress which can possibly exist at any point of a body may be produced by the joint action of three simple pull or push stresses in three suitably chosen di rections at right angles to each other. These three are called principal stresses, and their directions are called the axes of prin cipal stress. These axes have the important property that the intensity of stress along one of them is greater, and along another less, than in any other direction. These are called respectively the axes of greatest and least principal stresses. . . . In any condition of stress whatever the maximum intensity of shearing stress is equal to one-half the difference between the Introductory 7 greatest and least principal stresses and occurs on surfaces in clined at 45° to them. In any body the stress-difference at a given point is the difference between the maximum compressive stress and the minimum compressive stress at that point. St r e n g t h . In his book “Earthquakes and Mountains” (pp. 9, 10) H. Jeffreys wrote: The distortional stress needed to produce such permanent changes [flow and fracture] in a solid may be called its strength. . . . It is sufficiently accurate to say that failure is determined by the stress-difference. . . . In this work I shall always mean by the strength the stress-difference needed to produce deforma tion, whether it is flow or fracture. Elsewhere he phrased the matter thus: The critical stress-difference above which the rate of change of shape does not decrease when the time of application of the stress increases, may be called the strength of the material. . . . The plastic deformation in any element will cease when the stress- difference there sinks to the strength.* Describing experiments on the deformation of rocks, D. T. Griggs has illustrated both the need of expanding termi nology in discussion of terrestrial “strength,” and also the difficulty of securing in the laboratory precise values for this property. It is already clear that many solids are not rup tured or made to flow when exposed to high, unbalanced pressures for short periods, but are deformed permanently after being exposed to smaller stresses of the same kind, if these stresses are long continued. At atmospheric pressure rocks are brittle, and their strength is simply and easily measured and is found to be independent of time, at least to the limit of sensitivity of our measurements. Rocks under high pressure present a different problem. * H. Jeffreys, “The Earth,” 2nd edition, 1929, p. 180. Passage reprinted by permission of the Cambridge University Press and The Macmillan Company, publishers. 8 Introductory In measuring the strength of rocks under high confining pres sures we are confronted with the problem of choosing the point on the stress-strain curve that corresponds to the significant value for geological purposes. Two points are evident: (1) the elastic limit, or the limit of proportionality of the curve; (2) the ultimate strength, or the maximum stress supported by the rock before rupture occurs. Ultimate strength is here used as the mechanical engineers define the term. The adjective 'ultimate’ was applied by them to distinguish the final strength at the rupture point from the strength at the ‘yield point’. This usage is misleading because the ultimate strength is found to vary with the confining pressure and the duration of the test. The ‘elastic limit’ is changed only slightly by applying a con fining pressure to the specimen. Thus, a confining pressure of 10,000 atmospheres raises the elastic limit of the Solenhofen lime stone about 10 per cent. The ultimate strength, however, is very greatly changed by the confining pressure. . . . A pres sure of 10,000 atmospheres increases the ultimate compressive strength more than 600 per cent.2 On the other hand, Griggs found the ultimate strength of the limestone, at confining pressure of 10,000 atmospheres, to decrease rapidly during the first six hours and afterwards at a low and decreasing rate. The time-strength curve is of such a nature as to suggest that it is asymptotic to a certain value of strength at infinite time, which means simply that, if any force below this limiting value is applied to the rock for any finite time, the rock will not fail. There are not yet enough data to give more than a rough sugges tion that this might be true. It is to be hoped that future work will establish the time-strength relation so that it may be extra polated.3 If the curve becomes rectilinear and parallel to the time axis, under a maximum differential force, the co-ordinate for this part of the curve measures the kind of strength with which the geologist is most vitally concerned. For this Griggs Introductory 9 has coined the useful expression fundamental strength. His statement may be quoted: [The fundamental strength] of a body is the differential pressure which that body is able to withstand under given conditions of temperature and confining pressure without rupturing or de forming continuously.4 He notes that this idea would be more satisfactorily ex pressed by “ultimate strength,” which, however, has been pre-empted in a different sense by the engineers. Griggs has made preliminary but valued experiments on the creep of rocks and crystals sufficiently stressed for long periods, and has quantitatively separated “elastic” flow (diminishing) logarithmically with time) from “pseudo- viscous” flow (independent of time). As yet he has not been able to fix an absolute elastic limit for any kind of ma terial under high confining pressure. Geological time is long but finite. Conceivably there is no elastic limit for rock in a rigorous sense; yet the enormous duration of great inequalities in the earth’s topography proves the more su perficial rock formations at least to have what may be called practical strength. Solid. Any substance with practical strength may be called solid, even though the substance can not bear stress- difference for infinite time. This test for the solid state is not readily applied in the case of the deep earth-shells; hence Jeffreys adopts another criterion: any shell capable of trans mitting elastic waves of the distortional (transverse, shake) type is to be regarded as solid.5 This property means the possession of rigidity, but, as already remarked, rigidity it self is a relative property, depending on the amount and duration of the stress causing the elastic reactions necessary for transmission of the wave. Thus, from the velocities of sound in the hypersonic and ultrasonic ranges of frequencies, glycerine, a liquid as ordinarily conceived, has been found 10 Introductory to have a measurable, finite rigidity. Its viscosity is that of a normal liquid, and yet appears to be best explained by Maxwell’s theory of elasticoviscosity. In other words, the viscosity is a “fugitive elasticity.”6 It is, therefore, hard to follow Jeffreys when he recognizes the fluid state of a substance by the absence of rigidity and by the smallness of the viscosity in comparison with that in other states of the same material. Other states characterized by high viscosity, with or without rigidity and strength, will be called solid. Thus pitch at ordinary temperatures will be regarded as a solid. Jeffreys continues: It is possible, though not certain, that all solids possess rigidity. They may, however, be devoid of strength. There is only one state of solids in which they are quite lacking in strength. In this state they are amorphous and practically uniform throughout. There is another state, however, bearing at first sight a close resemblance to the last, in so far as solids in this state are also amorphous and uniform, but differing from it in the possession of considerable strength. Both states are com monly described as vitreous or glassy. The difference between them is so important, however, as to merit a difference of nomen clature. The former will here be called the liquevitreous and the latter the durovitreous state.7 Jeffreys regards “liquevitreous” and “elasticoviscous” as synonyms, and divides the fundamental states of matter into three classes: gaseous, crystalline, and vitreous. Greatly subcooled, artificial glass is “durovitreous.” On the other hand, Morey believes that there is no critical temperature at which glass exchanges the liquevitreous (strengthless) state for the durovitreous (strength-retaining) state.8 The two views are not necessarily in conflict, if cold glass is de formed under any minute, steady stress in shear at a rate that is finite but too small for measurement. It is another case where it may be necessary to distinguish between abso lute or fundamental strength and “practical” strength. Introductory 11
I so sta sy a n d R e l a t e d E x p r e s s io n s . For several dec ades, investigation of the strength in the earth’s outer shells has been guided by the study of a theoretical principle called isostasy. How the principle attained recognition will be stated in detail later, but it is expedient to note immediately the meaning of this comparatively new word. Isostasy may be regarded as a tendency and also as a condition. (1) On the one hand, isostasy is the tendency toward the disappearance of any stress-difference which, because of un equal loading, may have been developed in an earth-shell beginning a few scores of kilometers below sea level.* In other words, the pressure at any level within this shell tends to become hydrostatic, and, if the tendency is fully satisfied, the shell could be considered a liquid. This condition would be a feature of what may be called ideal isostasy; the weight of the material situated between the surface of the globe and some level in the “liquid” layer would be constant, no mat ter how varied the surface relief may be. At that level a vertical column under the surface of a high range of moun tains would have the same weight as the corresponding ver tical column under a low plain or the analogous vertical column under the water surface of the deep sea. Each column would be isostasios (Greek for “in equipoise”) with all the other columns. The uppermost level of uniform pressure at the bases of the balanced columns is called the * This phrasing is not that of Dutton, who coined the word “isostasy.” His definition and illustration of the principle are quoted in the next chapter. There he does emphasize the smallness of the depth where the weak shell begins, but makes no assumption regarding the thickness of this shell. However, as shall be noted in chapter 12, recent studies of the earth’s figure strongly suggest that the weak shell does not exceed a few hundreds of kilometers in thickness, and that the rest—much the greater part—of the silicate mantle overlying the earth’s “iron” core has considerable strength. If this be true, the departures of the earth from hydrostatic equilibrium may be of two kinds. The one kind is due to in equalities in the horizontal distribution of mass in the superficial shell that overlies the weak shell. The other kind may be due to inequalities of mass among seg ments of the thicker, strong shell that underlies the weak shell. In order to retain the essential idea named by Dutton and debated by geodesists and geologists dur ing the last fifty years, the present writer has defined “isostasy” somewhat differently from Dutton. 12 Introductory isopiestic level (literally, level of uniform pressure). See Figures 3, 4, and 9 (pp. 48, 61). The equality of pressure means, to a close approximation, equality of mass. Hence the rock underlying a high plateau and reaching down to the isopiestic level must, according to the hypothesis of isostasy, have a lower average density than the rock composing a column topped by the lower continen tal surface, and a fortiori a lower average density than a column topped by the ocean water. This relation of density to elevation of surface is conveniently phrased in these words: the earth’s relief is compensated by differences of density characterizing the rock above the isopiestic level, which may be also defined as the maximum depth of compen sation. The whole mass between the isopiestic level and the surfaces of lands and oceans is called the layer {or zone) of compensation for the topographic relief of the whole earth. If a continental column has a mass greater than that just sufficient to keep it in isostatic balance with the rest of the earth, that column is said to be undercompensated. If the condition is reversed, the column is said to be overcompen sated. If an oceanic column has a mass less than that giving isostatic balance, it is described as undercompensated, and the reverse condition means overcompensation. According to ideal isostasy, the unloading of a land sector of the globe by prolonged erosion is ultimately followed by return flow of matter within the deep, weak layer, so as to restore equality of pressure at the isopiestic level and sub stantial equality of mass in all columns above this level. Loading of a sector with detritus or with an icecap ulti mately causes flow in the deeper layer away from the loaded sector, until, here too, substantial equality of mass among all sectors is restored. Such movements of the deeper ma terial are, of course, accompanied by warping or other defor mation of the upper layer. The process of restoring balance is called isostatic adjustment. Introductory 13 It has been proved that considerable areas of the earth’s surface are underlain by rock with weight in. excess of that which, if propagated directly downward, would give bal anced, hydrostatic pressure in the underlying layer, sup posed, ideally, to be “fluid”; also that other segments of the upper layer lack sufficient mass and therefore weight to offset completely the upward pressure of the “fluid.” Further, these failures of balance have existed for millions of years, with no indication that the upper layer is losing any of its internal stress—which necessarily is considerable. Such duration of stress indicates what we have called “practical strength” for the lithosphere, and probably indi cates fundamental strength. The upper layer, capable of bearing “permanently” the stress-differences that are caused by contrasts of total mass in throughgoing, vertical columns, will here be referred to as the lithospheric shell or, more briefly, the lithosphere (rocky layer). Asthenosphere, an abbreviation of the formally more correct asthenospheric shell, is a useful name for the underlying, weak shell, though the word literally implies complete absence of strength. The terms do not connote anything with respect to the state of the asthenospheric material in the physico-chemical sense.* It is an open question whether the asthenosphere is a true fluid, but there is ample evidence that its viscosity is high when measured against small stress-differences. The viscos ity ensures that at any given moment, even if the astheno sphere has the properties assumed by the hypothesis of ideal isostasy, there must be in this earth-shell small but real de * Later, the facts suggesting the existence of a thick, strong layer underlying the weak asthenosphere will be described. That deep layer with considerable strength will be given the name suggested by H. S. Washington, namely mesosphere or its variant, mesospheric shell. These terms seem preferable to Barrell’s “cen- trosphere,” which would logically include also the iron core of the earth. Some seismologists doubt that the core has any strength, and in any case the major discontinuity at contact of core and mesospheric shell may be profitably empha sized in the nomenclature for the earth’s principal components. 14 Introductory partures from the hydrostatic condition. For the land seg ments of the lithosphere are being ceaselessly lightened by erosion, and the oceanic segments are being ceaselessly weighted by new loads of sediment, but the balancing of weights must be delayed by the viscosity of the lower layer. It seems clear, therefore, that the isostatic tendency is not now completely satisfied, and has never been satisfied, ever since the early Pre-Cambrian epoch when dry land began its steady featuring of the earth’s relief.* (2) On the other hand, most students of earth physics believe that the departure from ideal isostasy is compara tively small—that the asthenosphere is, in truth, extremely weak. Thus the word “isostasy” is used to express an ac tual condition of the earth’s outer shells as well as a tendency ruling those shells. The condition is one of approximate balance among the vertical, lithospheric columns in regions of high mountain, low plains, and deep oceans. While there is wide recognition of the principle, a gener ally acceptable definition of actual isostasy in quantitative terms is impossible. As yet no definite values can be as signed to the heights of the vertical columns that are sup posed to be in balance on the asthenosphere. Nor can definite values be assigned to the widths of those columns. And there is a third difficulty: when the balancing of columns is described as “approximate,” an evident lack of important information is implied. Thus the problem of isostasy, as actually represented in Nature, is multiple, and its ultimate solution must include determination of the heights and cross sections of the ver tical columns in balance, and also decision as to the existence and duration of stress-difference in the asthenosphere. If this lower layer does bear stress-difference indefinitely, no * The last statement in the text means that there is, strictly speaking, no isopiestic level in the earth, but the name is still useful in defining the smallest depth where the departure from the hydrostatic condition first becomes, in the earth as a whole, of negligible importance. Introductory 15 precise values can be stated for the heights of the overlying columns assumed to be in mutual balance. We are to see, however, that the asthenosphere is so weak that approxi mate limits for the strength of the lithosphere and for its thickness can be determined by applying the hypothesis of ideal isostasy in various forms. In fact, by making this ap plication the geodesists have tested the idea of actual isos tasy. Their results have proved most valuable when cor related with the data of seismology and general geology. The following chapters describe both methods and results, and also the relevant facts derived from dynamical geology. It is significant that the two kinds of testing agree in a gen eral conclusion: the lithosphere is relatively thin and decid edly strong, and the asthenosphere seems to be nearly or quite devoid of strength. Three other facts may be emphasized. First, it is highly improbable that the thickness, temperature, and strength of the lithosphere have been constant throughout geological time. Any secular change in that shell should have been accompanied by corresponding change in the physical prop erties of at least the upper part of the asthenosphere. In other words, the conditions of the present day with respect to the distribution of strength in the globe can not be as sumed to have ruled at earlier epochs, including those of in tense mountain-making or igneous action. Second, to prove the existence of a perfectly weak asthenosphere would be easier than to ascertain its exact thickness. Third, the prin ciple of isostasy does not imply any particular thicknesses, or any particular degrees of strength, for the layers beneath the asthenosphere. If it could be proved that the layer of compensation is strong because crystalline, and that the underlying layer is weak because it is too hot to crystallize, the names crust and substratum would be synonyms of lithosphere and astheno sphere respectively. But those simpler terms are not to be 16 Introductory preferred: first, because they imply a theory of the earth’s interior that is inacceptable to some of the ablest investiga tors of physical geology; and, secondly, because the word “crust” has been employed with a variety of other meanings. For example, some writers on isostasy mean by “crust” all that part of the earth’s mantle that is situated above the depth of compensation, while for others the word means that part of the superficial, rocky layer that has density decidedly smaller than the mean density at the same high range of levels. Such relatively light rock composes most of the formations visible over continents and large islands, and because of its individualization in the planet, has been named the sial (mnemonic for silica and alumina, abundant constituents of this material). Underneath is a much thicker composite layer called the sima (mnemonic for silica and magnesia, abundant constituents). Both geological and seismological observations indicate that the comparatively thin, conti nental sial is underlain by simatic material but also is island like and horizontally bounded on all sides by sima. In the continental sectors of the globe the sial and a layer of under lying sima, with comparable thickness, together constitute the lithosphere. In the oceanic sectors the lithosphere ap pears to be wholly or almost wholly simatic. The seismol ogists have shown that in general the asthenosphere is of simatic composition. DISCONTINUITIES IN THE EARTH Conclusions regarding the locus or loci of terrestrial strength depend on comparison of observed values of gravity with the distribution of attracting mass. To make the com parison, measurements of gravity are referred to the best available “figure of the earth,” as determined by the geode sists. The resulting values give important information about underground masses, but such data become more im Introductory 17 mediately trustworthy if they are found to agree with seis- mological and other geophysical discoveries regarding the anatomy of the earth. We shall now glance at the modern ideas as to the general constitution of the planet and, also in this introductory chapter, note the progress already made in the problem of describing its “figure” in the best way. The mass of the earth may be taken at 5.9 X 1027 grams and the mean density at 5.517. From geological and as tronomical observations a rough idea of the distribution of mass has been obtained, the result depending to a large ex tent on the seismologists’ discovery of systematic breaks or “discontinuities” in the terrestrial material. The location and relative importance of these breaks are questions which call for continuing investigation, but already much has been learned. At the surface the average density of the Basement (Archean) Complex of each continent is close to 2.70, while geophysicists generally assume 2.67 to be the average for all the rocks of the continents between the surface and a depth of the order of 10 kilometers. From both seismological and geological evidence, the density of the analogous layer under the deep ocean is believed to be nearly 3.0. The ocean, with mean depth of about 3,700 meters, has a density of 1.027. Below the continental surfaces and above a level 50 kilo meters deeper, a number of discontinuities of density have been demonstrated. An obvious type is that in which sedi ments, with their characteristically lower density, rest on the Basement Complex, but the crystalline sial itself shows at least one break, and still deeper—yet still above the 50- kilometer level—a more drastic increase of density must be assumed. The exact depths of the discontinuities just de scribed are not easily demonstrated, and it seems clear that each of the breaks varies in its depth below the rocky surface. However, a normal section through the sial may be de 18 Introductory scribed, using round numbers, as essentially composed of a superficial “granitic” layer with average density of 2.70 and thickness of 15 kilometers, and an underlying, “intermedi ate” 25-kilometer layer of less silicious, more “basic,” rock with average density of about 2.9. Opinions differ as to the density and chemical composition of the rock below the second or 40-kilometer discontinuity. Some geophysicists suppose this third principal layer under the continental sur faces to be crystalline dunite or some other “ultra-basic” type, but a “gabbroic” composition seems more probable.* Jeffreys is a leader among those who assume not only an “ultra-basic” composition but also crystallinity for the third layer, even to the depth of many hundreds of kilometers. The present writer has summarized the objections to this view, and has preferred the working hypothesis that the “gabbroic” layer under the continents averages about 20 kilometers in thickness and rests upon a vitreous, basaltic shell. See Figure 9, p. 61. That hypothesis, developed as a basis for understanding the earth’s igneous activities during the last billion years and for understanding the facts of dynamical geology in general, calls for testing by the seismological method, combined with measurements of the elastic moduli of rock glass at the as sumed high temperature and high pressure. For two rea sons this test is hard to make. Owing to uncertainty about the thickness of, and wave- velocities in, the different sub-layers of the lithosphere, it is still impossible to state exact values for the velocity of the longitudinal wave between —50 and —100 kilometers, or to establish the actual rate of change of the velocity between those two levels. Nevertheless, Gutenberg has found evi * See R. A. Daly, Amer. Jour. Science, vol. 15, 1928, p. 108; “Igneous Rocks and the Depths of the Earth,” New York, 1933, p. 173; and “Architecture of the Earth,” New_York, 1938, p. 42. In average the third layer may be somewhat more “basic” than gabbro, and at the high pressure charged with minerals having lower average compressibility than the minerals in ordinary gabbro. Introductory 19 dence of a change of wave-velocity at a depth of 60-70 kilo meters, and in 1939 Gutenberg and Richter reported new indications that the material below the depth of 60 to 80 kilometers from the earth’s surface may be in the “glassy condition.” 9 The second difficulty, that of measuring satisfactorily the elastic moduli of rock glass at a temperature exceeding 1,200° C. and at pressure exceeding 16,000 atmospheres, is apparent. The compressibilities of tachylite and artificial diabase glass at room temperature have been independently got by L. H. Adams, F. Birch, and P. W. Bridgman. Birch has measured the elastic moduli of artificial diabase glass at temperatures ranging up to 300° (results unpublished). From the values obtained it now seems improbable that a thick, world-circling, vitreous layer of average basalt or even average plateau-basalt is now present in the earth. How ever, a relatively thin, interrupted couche of either kind of material is not excluded. The wave-velocities announced for the material constitut ing a continuous shell between the 60-kilometer and 80- kilometer levels under a continent appear to correspond well with vitreous oceanite (or vitreous ankaramite). Oceanite is a basalt with a composition about halfway between those of average basalt and average peridotite. A vitreous state for the asthenosphere accounts easily for the demonstrably great weakness of this earth-shell.* The * Some geophysicists explain the weakness by supposing that the asthenosphere is made of crystallized peridotite at or close to the temperature of melting, and, secondly, that at such temperature crystallized peridotite has practically no strength. The second assumption is made on thermodynamic grounds, but it can hardly be correct if the temperature is even a few degrees below that of melting. The first assumption implies a highly improbable adjustment between thermal gradient and source of heat in the earth. If the furnace effect of radioactivity is a reality, is it even conceivable that, after the lapse of more than a billion years, the asthenospheric rock can be so nicely tempered? One would expect the mean temperature of the material to be either well above or well below the temperature of melting. The first of these two alternatives has the advantage that it solves the problem of asthenospheric weakness in a way that does not involve an in credible law for the distribution of underground heat. 20 Introductory assumption that, below some such depth as 80 kilometers, oceanitic glass passes down into vitreous peridotite gives a theoretical basis for understanding the dikes of peridotite in Arkansas, Kentucky, New York State, and elsewhere; the kimberlite pipes and dikes of South Africa; and the volumi nous ophiolites, peridotites, and serpentines that were in jected into the mountain-roots of New Caledonia, Celebes, New Zealand, and other disturbed parts of the lithosphere. Detailed discussion of these genetic relations will not be attempted on the present occasion.* The seismologists have discovered no definite discon tinuity between the 80-kilometer level and that of the dis continuity located by Jeffreys at the approximate depth of 480 kilometers.10 This change in the terrestrial material will be referred to under the name “Jeffreys discontinuity.” In chapter 12 we shall have occasion to inquire into its nature. Under the deeper parts of the ocean, the seismologists have been unable to find evidence for sialic rock, like that constituting the granitic and intermediate layers of the con tinental sectors. The wave-velocities in the rock just below the oceanic ooze, under the deepest parts of the Pacific at least, are appropriate for crystallized basalt, gabbro, or dia base. As yet no discontinuities have been demonstrated in the rock near the surface, but this does not mean that none exists there. The matter needs investigation. Perhaps the establishment of a sufficient number of seismological sta tions, properly placed along the row of Hawaiian islands, * If the crystallized lithosphere has been slowly thickening, the uppermost world-circling sub-layer of the asthenosphere has had, during the march of geo logical time, an average composition less “basic” than oceanite. When stressing the relevant geological facts, the writer was led to prefer a composition like that of ordinary plateau-basalt for the world-circling and eruptible sub-layer existing through most of the last billion years. That preference is not essentially weakened by the new experimental evidence that the uppermost, world-circling sub-layer of the asthenosphere at the present epoch is as dense as oceanite. Introductory 21 may lead to the much-desired answer to the question. Meanwhile, thought can be guided to some extent by the fact that seismograms seem to prove nearly perfect homogeneity along each level within the earth-shell included between the 100-kilometer and 400-kilometer levels, and extending under continents and oceans alike. Incidentally we note that the seismological data regarding the contrast of the rocky materials respectively underlying continental surface and ocean floor go far toward demon strating a high degree of general isostasy. Gutenberg and Richter explain the travel-times of the longitudinal and transverse, seismic waves by postulating a discontinuity at the depth of about 1,000 kilometers and two other discontinuities near the 2,000-kilometer level.11 Other authorities, including Jeffreys, find no clear indication of any break between the Jeffreys discontinuity at about —480 kilometers and that at the depth of about 2,900 kilo meters (2,920 kilometers in Bullen’s table to follow), where there is the most pronounced break of all, an interface or rapid transition between the earth’s silicate mantle and its “iron” core. CALCULATED INTERNAL DENSITIES Using values for surface density, mean density, and depths of discontinuities, as well as the known value of the earth’s moment of inertia, different investigators have computed what the densities should be at all depths from the surface to the center of the globe. The results differ according to the densities assumed at the surface and within the iron core, according to the range of depths assumed for the discontinui ties, and according to the range of assumptions regarding the rate of increase of density in each shell. Clearly each of these premises is to some degree uncertain, and the calcula 22 Introductory tions can give only a crude picture of the reality. Yet a few examples will show how the problem has been narrowed in spite of all uncertainties. Klussmann, postulating discontinuities at depths of 1,200 and 2,450 kilometers, based his computation on the simplify ing and incorrect assumption that the two shells and the iron core (this beginning at 2,450 kilometers) are of uniform density. Taking 3.0 (case A) and then 3.2 (case B) for the density of the outer shell, he found the densities of the other shell and the core to have the values here shown: DENSITIES Case A Case B Shell between 0 km and 1,200 km 3.0 3.2 Shell between 1,200 km and 2,450 km 7.2 6.6 Core between 2,450 km and 6,370 km (center) 8.3 8.8 Gutenberg assumed discontinuities at the depths of 60, 1,200, 1,700, 2,450, and 2,900 kilometers; density of 3.5 at the 60-kilometer level; uniform density in the core; and in crease of density in the uppermost and lowermost shells. His results were: DEPTH (km) DENSITY 60...... 3.5 (steady increase to 1,200 km) 1,200 ...... 4.75] 1,700 ...... 4.75 > no change 2,450 ...... 4.75J (steady increase to 2,900 km) 2.900 (base of silicate matter) ...... 5 2.900 (top of iron core)...... 6,370 (center)...... } J > no change Recently Bullen, accepting Jeffreys’ discontinuity at the depth of 481 kilometers (about 474 kilometers, according to Jeffreys’ later investigation), assuming the top of the iron core to be at a 2,920-kilometer level, and taking 3.32 as the Introductory 23 density just below a 42-kilometer discontinuity, obtained the following values: DEPTH (km) DENSITY (nearly steady increase between levels given, except at the two discontinuities) 42...... 3.32 100...... 3.37 200...... 3.46 400 ...... 3.63 481 (above)...... 3.69 481 (below)...... 4.23 500...... 4.25 800 ...... 4.45 1,600...... 4.91 2,400...... 5.31 2.920 (above)...... 5.56 2.920 (below)...... 9.69 3,000...... 9.82 3,200...... 10.13 6,371 (center)...... 12.17 Bullen’s rate of increase of density between the depths of 42 and 481 kilometers is nearly equal to that which would result from the earth’s self-compression, this layer of ma terial being chemically homogeneous. A similar relation applies to the layer of different, intrinsically denser material between the depths of 481 and 2,930 kilometers, as well as to the iron core below the 3,000-kilometer level. It is highly probable, however, that the intrinsic, or chemically determined, density of the two silicate shells increases with depth after the fashion illustrated in thick sills and lopoliths. If this be true, the initial density at the 42-kilometer level and also the range of densities down to the 481-kilometer level may be considerably smaller than the respective den sities tabulated and yet satisfy the condition set by the mo ment of inertia. Later we shall see how important is the question here raised. In reality, it appears that a minimum density of 3.32 for the material between the 42-kilometer and 100-kilometer levels is irreconcilable with many principal facts of dynamical geology. Before leaving this latest and best discussion of the earth’s 24 Introductory internal density, we may note some other data from Bullen’s paper, though these will not be directly used in the following discussions. For 0.334 Ma2, the earth’s moment of inertia (radius is a), he gives 80.6 X 1043 gram-cm2. The moments for an assumed 11-kilometer granitic shell, a 24-kilometer intermediate shell just below it, and the iron core came out respectively12 at 0.39 X 1043, 0.93 X 1043, and 8.58 X 1043. FIGURE OF THE EARTH: GEOID, ELLIPSOID, SPHEROID In order that measurements of the intensity and direction of gravity shall give information about the distribution of strength, it is necessary to know as accurately as possible the true configuration of the planet. The required informa tion is got by comparing the deflections of the plumb line at many different stations, and also by comparing the values of the force of gravity at many different stations. The solu tion of the problem demands statistical analysis and there fore reduction of the instrumentally determined values to common denominators. Deflections of the plumb line can be usefully compared only if their values be recalculated in terms of a single level of reference. So it is also with fruitful comparison of the intensities of gravity. Manifestly the actual, more or less rugged surface of the globe will not serve as a basis for these comparisons. In deed, there is no such thing as a strictly definable shape of the earth in a physical sense. This is obvious when we think of the eternal dance of the atmosphere and ocean water. Even the solid earth changes every second as rivers, winds, and ocean waves keep moving particles of the super ficial rock, with prompt elastic distortion of the solid earth as its surface loads are thus shifted about. On the other hand, Nature has provided a natural surface of reference in the form of mean sea level, the position of which can be closely determined at and outside the limits of continents and islands. Continued under the land masses Introductory 25 this level is a world-circling, equipotential surface, so impor tant for geodesy and geophysics that Listing’s special name for it, geoid, has been universally adopted for practical use.13 The depth of the geoid below the surfaces of the lands is not known with absolute accuracy. As a whole, it has a com plicated, wavy shape. Hence for the purposes of geodesy simpler, mathematically described figures, departing as little as possible from the geoid, have been computed. Theory shows that the geoid can not in any case be an exact ellipsoid of revolution—that is, the figure generated by the rotation of a perfect ellipse about its minor axis (cor responding to the earth’s axis of rotation). Nevertheless, geodesists find practical advantage in adopting a formula of a rotational ellipsoid, a mathematical fiction, as a convenient, approximate expression for the “figure of the earth.” A still closer approximation is reached when the ellipsoid of revolution is modified by slight east-west depressions with trough-lines circling the globe at 45° north latitude and 45° south latitude. In other words, the spherical surface is now supposed to be modified by the second-degree harmonic of the equatorial bulge, and then to a fourth-degree harmonic with crests at poles and equator and troughs at mid-lati tudes. In making subsequent references we shall distin guish the more complicated figure under the name spheroid of revolution. Like the ellipsoid of revolution, it has a circular equator. However, study of the variation of gravity over the earth seems to show that the geoidal equator is not a circle but approximately an ellipse, with a small departure from circu larity. Hence geodesists are now discussing the dimensions of the best triaxial ellipsoid and the best triaxial spheroid to represent the actual geoidal figure, the respective names meaning absence or presence of the mid-latitude depressions of the surface.* * The definitions of “ellipsoid” and “spheroid” implied in the text are not uni 26 Introductory In summary, then, the shape of the earth may be thought of as: 1. The actually diversified physical surface, which is strongly accidented by alternating lands and bodies of water; 2. Or as the geoid\ 3. Or as a simplified, mathematical figure with the geometrical properties of: a. An ellipsoid of revolution; b. Or a rotational spheroid; c. Or £ triaxial ellipsoid; d. Or a triaxial spheroid. These various conceptions are so vital to our present in vestigation that a brief glance at the history of their develop ment may be taken. The first outstanding attempt to find the size of the earth was made by the Greeks before Aristotle. Eratosthenes, assuming the planet to be a perfect sphere, showed how the size could be calculated. The shortest distance between two stations along a meridian at the surface is measured. The angles made by the plumb lines or verticals at the two sta tions is determined by observations on sun or star, each of which is so far away that its rays are sensibly parallel. From these observations the circumference and radius of the sphere are easily computed. Newton proved that on account of rotation the shape of the sea level can not be spherical, but must be a nearly per fect ellipsoid of revolution. If the shape were that of an exact ellipsoid, its dimensions could be determined by suffi ciently accurate measurement of the linear separations of three stations on a meridian, and corresponding, accurate measurement of the angle made by each station zenith with a given star when on the meridian plane. Or the ellipticity and major axis of the generating ellipse could be found, if versally adopted by the geodesists or the mathematicians. The distinction is somewhat arbitrary, but is here made in the interest of clearness. Introductory 27 the lengths of degrees of latitude in well-separated zones of latitude were measured. But, because the earth’s surface is rough and because the constituent materials vary in density both horizontally and vertically, the plumb line is rarely normal to any strictly ellipsoidal surface. The de partures are usually large enough to defeat the searcher for the earth’s exact shape and size, if his data are restricted to those from a few stations. He approaches the truth more and more closely as the number of stations geodetically occu pied increases. Thus, when the resources of statistical mathematics are added to those of geometry, the geoid can be constructed with ever-increasing nicety. The precise methods of modern times have permitted measurement of many meridional, partial sections of the globe. In each section the sea level has been shown to deviate but slightly from the curvature of a perfect ellipse. Moreover, the various ellipses of comparison have nearly the same dimensions in the sections actually investigated— nearly, but not quite. If all meridional sections were proved similar, with con stant values for the ellipticity and length of polar axis, all sections along parallels of latitude would be circles, and the problem of the earth’s shape and size would be relatively simple. The actual irregularities found in meridional sec tions early suggested that there are irregularities also in lati tudinal sections; hence measurements of degrees of longitude are needed. These supplementary determinations could not be made sufficiently accurate until the electric telegraph and, later, radiosignaling, supplied the means of precisely measuring time and therefore arcs along any parallel of latitude. Al ready it has become known that the lengths of degrees of longitude, like those of latitude, vary but little—but we are to see that both types of variation may be significant for the 28 Introductory geophysicist, whose job it is to plumb the depths of the earth and detect the nature of the material there. The situation is somewhat ironical. The departures of the geoid from any assigned geometrical form must be meas ured with all possible accuracy, and from many such meas urements the assumed form is modified so as to reduce the departures to a minimum average value. In other words, a figure of the earth has to be assumed in order to find the figure of the earth. However, as already stated, this logical trouble is being gradually lessened by using the method of successive approximations. As early as 1841, Bessel was able to give the elements of an ellipsoid which was not very far from meeting the require ments for precise mapping of the globe. In 1866, Clarke, who had the advantage of additional data—though, like Bessel’s, largely confined to the Old World—announced a slightly different formula for the ellipsoidal figure. Forty years later this was used by Hayford as the basis for a new computation of the best ellipsoid to fit American observa tions made before the year 1906. Hayford published his new formula in 1909. In absolute measure it differed from Clarke’s but little—yet enough to warrant continued field work in the United States. After thirty more years the re sults prove the necessity of a small change in the Hayford 1909 formula, especially when the many measurements out side the United States are taken into consideration. The direction and amount of the change recommended by the International Geodetic Commission will be later indicated. While the standard ellipsoid or ellipsoid of reference (a mathematical fiction) is at the foundation of modern car tography, geodetic measurements of heights, depths, and geographical position are actually made with reference to the wavy geoid. Where there is a limited region with excess of density near the surface, or where there is a large area of high land, the sea water is drawn up along the borders of Introductory 29 that region, giving a localized hump on the terrestrial ellip soid. Where there is regional deficiency of mass near the surface, or where there is an extensive topographic basin, the sea level is hollowed below the ellipsoid. There is another reason why the geoid departs from any ellipsoid. Because the earth is rotating, and because its density increases from the surface downward, the sea level between each pole and the equator must be slightly depressed below the surface of an ellipsoid with appropriate axes. (See p. 25.) Hence, even if there were no irregularities in the superficial distribution of attracting mass, the sea level would, in relation to an ellipsoid, be slightly hollowed in the mid-latitude zones. The mathematician would describe such a figure as an ellipsoid modified by a harmonic of the fourth degree. An exact ellipsoid is a sphere modified only by a harmonic of the second degree. The harmonic of the fourth degree is contained in the geoid, but as yet it can not be measured by values derived from study of the deflections of the plumb line. On the other hand, theory gives a fairly accurate picture of the har monic, so that all recent gravity formulas for the figure of the earth include a corresponding term. Table 1 states the dimensions of ellipsoids of reference that have been computed by outstanding geodesists between the years 1841 and 1938. It is seen that the calculated ele ments have changed but little during the last 75 years of research, and have changed still less since Hayford, in 1909, reported the results of his work on deflections of the plumb line at hundreds of American stations. However, we note the aberrant quality of the ellipsoid computed, from Indian data alone, by the Survey of India and quoted by Hunter in 1932. The causes of this contrast with all the other ellip soids of reference will be considered later. It is worth noting that purely astronomical methods give values of the flattening which approach those tabulated. 30 Introductory From the moon’s motion E. W. Brown obtained the recip rocal 293.7, a value subject to some uncertainty because of ignorance as to the exact shape of the moon. The luni-solar precession of the equinoxes provides a more accurate way of measuring the average ellipticity; by this method Veron- net found the reciprocal to be 297.12 ± 1.0, and de Sitter 296.96 ± 0.10.14
T able 1 SUCCESSIVELY DERIVED (ROTATIONAL) ELLIPSOIDS OF REFERENCE
Investigator and date Equatorial radius, a Polar radius, b a/{a — b). reciprocal of publication (meters) (meters) of the flattening Delambre, 1800 6,375,653 6,356,564 334 Schmidt, 1830 6,376,945 6,355,521 297.6 Everest, 1830 6,377,253 — 300.8 Bessel, 1841 6,377,397 6,356,079 299.2 Pratt, 1863 6,378,245 6,356,643 295.3 Clarke, 1866 6,378,206 6,356,584 295.0 Clarke, 1880 6,378,249 6,356,515 293.5 Helmert, 1906 6,378,140 6,356,758 298.3 Hayford, 1906 6,378,283 6,356,868 297.8 Hayford, 1909 6,378,388 6,356,909 297.0 Heiskanen, 1926 6,378,397 6,356,921 297.0 (International), 1924 6,378,388 6,356,912 297.0 Hunter (India), 1932 6,378,509 — 292.4 Heiskanen, 1938 — — 298.3 A third astronomical method is based on the lunar paral lax, as measured, for example, by observations at Green wich and Capetown, which lie nearly in the same meridian. Assuming the best value for the equatorial radius, the flat tening along that particular meridian has been computed by de Sitter, who deduced the reciprocal 293.5. The difference from the more probable value for the earth as a whole has suggested to Lambert the possibility that “the meridians in the neighborhood of Greenwich are really flatter than the average, just as the gravity-formula with Helmert’s or Heiskanen’s longitude-term would make them.” 15 See p. 32. Introductory 31 From the variation of latitude (Chandler motion of the pole of rotation), Lambert has calculated roughly the posi tion of the larger principal equatorial moment of inertia, finding it to be not far from the position given by Helmert’s triaxial figure of the earth.16 (See Table 2.) Table 2 gives the coefficients, c0 to c4, in the equation for normal gravity (y0) at the surface of each of the prin-
T able 2 ELEMENTS OF SUCCESSIVELY DERIVED SPHEROIDS
Difference Investigator and date of semi-axes of publication C0 ci C3 ci of equator (meters) Helmert, 1884 978.000 0.005310 ______Helmert, 1901 .030 5302 0.000007 — — — Bowie, 1912 .038 5302 << — — — Helmert, 1915 .052 5285 u 0.000018 + 17° 230 Berroth, 1916 .046 5296 a 0.000012 + 10° 150 £< — — Bowie, 1917 .039 5294 it — Heiskanen, 1924 .052 5285 ii 0.000027 -18° 345 Heiskanen, 1928 .049 5293 i( 0.000019 0° 242 Heiskanen, 1928 .049 5289 — — — International, 1930 .049 52884 0.0000059 — — — Survey of India (II) 1932 .025 5234 0.000006 Hirvonen, 1933 — — — — + 19° 139 Heiskanen, 1938 .0451 53027 0.0000059 — — — Heiskanen, 1938 .0524 5297 (< 0.0000276 + 25° 352 cipal spheroids of reference proposed since the year 1883. In its most general form the equation reads:
7o = c0 [1 + ci sin2
R efer en c e s 1. W. J. M. Rankine, Miscellaneous Scientific Papers, London, 1881. See also the references to Rankine in “A History of the Elasticity and Strength of Materials,” by I. Todhunter and K. Pearson, Cambridge, Eng., vol. 2, 1893. 2. D. T. Griggs, Jour. Geology, vol. 44, 1936, p. 557. 3. D. T. Griggs, op. cit., p. 560. 4. D. T. Griggs, op. cit., p. 541. 5. H. Jeffreys, “Earthquakes and Mountains,” London, 1935, p. 25. Introductory 35 6. C. V. Raman and C. S. Venkateswaran, Nature, vol. 143, 1939, p. 798. 7. H. Jeffreys, “The Earth,” second edition, p. 183. Cam bridge, Eng.: Cambridge University Press, 1929. Re printed by permission of the Cambridge University Press and The Macmillan Company, publishers. 8. G. W. Morey, Jour. Amer. Chem. Soc., vol. 17, 1934, pp. 315, 323. 9. B. Gutenberg and C. F. Richter, Science, vol. 90, Science Supp., 1939, p. 6; Bull. Seism. Soc. America, vol. 29, 1939, p. 531. 10. See H. Jeffreys, Mon. Not. Roy. Astr. Soc., Geophys. Supp., vol. 3, 1936, p. 346. 11. B. Gutenberg and C. F. Richter, Gerlands Beitraege zur Geophysik, vol. 45, 1935, p. 349, and vol. 47, 1936, p. 129. 12. See W. Klussmann, Gerlands Beitraege zur Geophysik, vol. 14, 1915, p. 1; B. Gutenberg, “Der Aufbau der Erde,” Ber lin, 1925, p. 44; and K. E. Bullen, Mon. Not. Roy. Astr. Soc., Geophys. Supp., vol. 3, 1936, p. 395. 13. See Nachr. kon. Gesell. Gottingen, 1873, p. 41. 14. See W. D. Lambert, Amer. Jour. Science, vol. 18, 1929, p. 155. 15. W. D. Lambert, op. oil., p. 157. 16. W. D. Lambert, Jour. Washington Acad. Sciences, vol. 12, 1922, p. 42; Special Publication 80, U. S. Coast and Geo detic Survey, 1922, p. 70; Amer. Jour. Science, vol. 18, 1929, p. 162. 2 DEVELOPMENT OF THE IDEA OF ISOSTASY
The name “isostasy” was invented in 1889 by Dutton, a geologist, but its underlying principle was familiar to geode sists long before that time. BOUGUER TO PETIT Between the years 1735 and 1745, a French party, includ ing Pierre Bouguer, measured a meridian arc in Peru. One result of this famous expedition was Bouguer’s book, “La Figure de la Terre” (Paris, 1749). He there expressed the conviction that the gravitational attraction of the lofty Andes “is much smaller than that expected from the mass of matter represented in those mountains.” R. J. Boscovich gave in Latin (1755) and French (1770) an explanation of the fact noted by Bouguer. A free translation from the French text reads as follows: The mountains, I think, are to be explained chiefly as due to the thermal expansion of material in depth, whereby the rocky layers near the surface are lifted up. This uplifting does not mean the inflow or addition of material at depth; the void {“vide") within the mountain compensates (“compense”) for the overlying mass.1 Thus Boscovich, long before Pratt (see below), postulated attenuation of the matter below a mountain range, sufficient to compensate largely for the extra height of that range. He also concluded that the earth-shell characterized by such 36 D evelopment of Idea of Isostasy 37 attenuation is relatively thin, as expressly implied by the modern word “isostasy.” The passage quoted marks per haps the first appearance of the verb “compensate” (“com- pense”) in connection with our subject. The compensation for the extra height of a mountain range was thought by Boscovich to be the effect of a dynamic process—expansion of the rock underlying the mountainous surface. But in passing we note a second important cause for the steady support of high topography. If relatively light rocks are moved horizontally so as to accumulate and grow thicker in any area, the surface of the whole concentrated mass must stand, when in isostatic equilibrium, higher than the surface of the surrounding, heavier rocks. This will be true whether there be subsequent attenuation by local heat ing or not. The support of the topographic relief is here due to a static condition—the composition of the rocks concerned—rather than to a change of their volume. It was reserved for Airy, in 1855, to find in rock composition the second reason why isostasy is so nearly perfect. By the year 1830, geologists already had proved that enormous masses of rock had been eroded off the continents and deposited far away, in oceanic or other basins. Appar ently no one of them had asked the question whether the earth’s body responded so fully to the shifts of load that hydrostatic balance in the deep interior was wholly or partly restored. In a letter dated February 20, 1836, Sir John Herschel, astronomer, answered the question in t'he affirma tive. By means of a diagrammatic cross section he showed how the outermost earth-shell is depressed by the weight of an added, wide prism of sedimentary rock. The depression is permitted by the earth’s plasticity. Beneath the prism, at comparatively shallow depth, rock matter flows out hori zontally in all directions, with corresponding subsidence of the prism and its floor. Herschel wrote: “Lay a weight on a surface of soft clay; you depress it below, and raise it 38 D evelopment of Idea of Isostasy around the weight,” and continued: “the removal of matter from above, to below, the sea . . . produces a mechanical subversion of the equilibrium of pressure.” * Thus Herschel enunciated another prime feature of the isostatic theory—the essential mechanism now called “iso static adjustment,” that is, Nature’s method of annulling temporary departure from isostatic balance. It has been repeatedly stated that Babbage had grasped the idea of isostasy—but stated without good reason, as Knopf and Longwell have shown. What Babbage actually did was to emphasize the vertical expansion of rocks when locally heated by the rise of the isotherms, that is, the ther mal attenuation which Boscovich had considered long before.2 In 1849, F. Petit had proved that the astronomic and geodetic latitudes of Toulouse agreed more closely than they should if the high Pyrenees mountains were an extra mass piled on the earth, otherwise in equilibrium. In explana tion he suggested that there is deficiency of attracting mass, a “void,” in the mountainous body—Bouguer’s conception for the Andes a century before. Petit did not clearly state the depth to which the deficiency of mass extends below the surface of the Pyrenees, so that, like Boscovich, he antici pated only in part the hypothesis later proposed by Pratt for a similar set of facts in India.3 PRATT The situation in India became clear after Everest had completed his great triangulation. He found that the geo detic latitudes of Kaliana station and Kalianpur station, * J. Herschel, in C. Babbage’s Ninth Bridgewater Treatise, Appendix to second edition, London, 1838, pp. 234-5. Compare J. Herschel, Proc. Geol. Soc. London, vol. 2, 1837, p. 597, where the author advocated the idea that the earth has a thin crust resting on a planetary core too hot to crystallize and therefore mobile enough to flow away from sectors newly loaded with sediment. See also the same author’s “Physical Geography,” second edition (Edinburgh, 1862), p. 116. D evelopment of Idea of Isostasy 39 375 miles south of Kaliana—both in northern India—differ by 5° 23' 42".294, while their astronomic latitudes differ by
F igure 1. The geographical relations of peninsular India, Indo-Gangetic plain, and High Asia; also location of_geodetic stations at Kaliana, Kalianpur, and Damaridga. 5° 23' 37".058. (See Figure 1.) Hence the two differences themselves differ by 5".236. J. H. Pratt concluded that 40 D evelopment oe Idea of Isostasy the difference 5".236 must . . . be attributed to some other cause than error in the geodetic operations. A very probable cause is the attraction of the superficial matter which lies in such abundance on the north of the Indian arc. This disturbing cause acts in the right direction; for the tendency of the mountain mass must be to draw the lead of the plumb line at the northern ex tremity of the arc more to the north than at the southern extrem ity, which is further removed from the attracting mass. Hence the effect of the attraction will be to lessen the difference of lati tude, which is the effect observed. Whether this cause will ac count for the error in the difference of latitude in quantity, as well as in direction, remains to be considered. Pratt summarized a preliminary discussion: It appears to me to be unquestionable that the geodetic opera tions are in no way sensibly affected by mountain attraction, and therefore need no correction whatever on that account. It is the astronomical operation of observing the difference of latitude which requires the correction. That it is here that the correction must be applied appears again in attempting to determine the azimuths of the arc astronomically. It is only when the plumb line is brought into use to determine the vertical angles of stars that the effect of attraction becomes sensible; and never in the geodetic calculations, where only horizontal angles or extremely minute vertical angles . . . are observed. Having thus cleared the ground for his quantitative study, Pratt proceeded to describe how the deflecting influence of High Asia (Himalaya-Tibet) on the plumb line at Kaliana and Kalianpur can be calculated. He found the deflection so occasioned at Kaliana to be 27".853, and that at Kalian pur 11".968. The difference between the two is 15".885, or nearly three times the observed contrast of 5".236 in the differences between the geodetic and astronomic latitudes at the two stations.4 Hence about two thirds of the hori zontal attraction of High Asia on the named Indian stations, computed from sea level upward, is offset either by deficiency of mass in the earth sector topped by High Asia, or by an excess of mass in the earth sector south of those stations in D evelopment of Idea of Isostasy 41 northern India. For the first time geophysicists were sup plied with a fairly accurate idea as to how great might be the effect of horizontal variation of rock density on the di rection of the plumb line. A principle that had been more abstractly stated by Bouguer and Petit now became illus trated in an epoch-making, quantitative way. In his 1855 paper Pratt hardly touched the question of the cause for the horizontal variation of density. Yet he did hint at his ultimate conclusion on that subject. He wrote: “Gradual changes of elevation and depression [of the earth’s solid surface] are unceasingly taking place in the sur face, arising no doubt from chemical and mineralogical changes in the mass” (p. 95 of his paper). Four years later he published a second important paper on the subject, where he stated his conclusion more defi nitely: At the time when the Earth had just ceased to be wholly fluid, the form must have been that of a perfect spheroid, with no mountains and valleys nor ocean-hollows. As the crust formed, and grew continually thicker, contractions and expansions may have taken place in any of its parts, so as to depress and elevate the corresponding portions of the surface. If these changes took place chiefly in a vertical direction, then at any epoch a vertical line drawn down to a sufficient depth from any place in the sur face will pass through a mass of matter which has remained the same in amount all through the changes. By the process of ex pansion the mountains have been forced up, and the mass thus raised above the level has produced a corresponding attenuation of matter below. This attenuation is most likely very trifling, as it probably exists to great depth. Whether this cause will produce a sufficient amount of compensation can be determined only by submitting it to calculation, which I proceed to do. . . . I can conceive of a vast tract beneath in which the develop ment of local heat had by long action expanded the material of the mass, and compressed it in a region beyond where no suffi cient heat was developed to counteract this effect.® As we shall see, thermal attenuation seems best to account 42 D evelopment of Idea of Isostasy for the excessive height of many plateaus, both mountain- structured and not. Pratt found by calculation that if the attenuation under High Asia extends uniformly to the depth of about 100 miles, the meridian deflections of the plumb line at the northern stations in India would be reduced to zero. He gave the value to illustrate what he described as a promising but unproved hypothesis. In later papers Pratt returned to the Indian problem, then taking account of the relatively weak attraction of the ocean water south of the peninsula, as well as the attraction of High Asia. The combined attractions again failed to ac count for the observed differences of latitude between suc cessive pairs of stations along the meridional arc of India. He left the problem open but offered two explanations of hypothetical nature: (1) by assuming a two per cent excess of density to the depth of about 200 miles under a circular area centering around a mid-point between Kaliana and Damaridga (a station about 800 miles south of Kaliana); (2) by assuming a defect of mass beneath High Asia and a similar defect south of Damaridga, toward Cape Comorin and the ocean. He thought the first hypothesis to be a safer guide to the “Hidden Cause.”6 AIRY Pratt read his first paper before the Royal Society of Lon don on December 7, 1854. On January 25, 1855, Airy sent to the Society a brief but equally classic essay on the Indian puzzle.7 After confessing surprise “that the attraction of the mountain-ground, thus computed on the theory of gravi tation, is considerably greater than is necessary to explain the anomalies [deflection residuals] observed,” he added: Yet, upon considering the theory of the earth’s figure as affected by disturbing causes, with the aid of the best physical hypothesis (imperfect as it must be) which I am able to apply to it, it ap pears to me, not only that there is nothing surprising in Arch deacon Pratt’s conclusion, but that it ought to have been antic D evelopment oe Idea of Isostasy 43 ipated; and that, instead of expecting a positive effect of attrac tion of a large mountain mass upon a station at a considerable distance from it, we ought to be prepared to expect no effect whatever, or in some cases even a small negative effect. Airy’s elaboration of this thesis is so significant in the his tory of the isostatic idea that full quotation is warranted, especially also because the original paper is not in the posses sion of most students of earth science. We read: Although the surface of the earth consists everywhere of a hard crust, with only enough water lying upon it to give us every where a couche de niveau, and to enable us to estimate the heights of the mountains in some places, and the depths of the basins in others; yet the smallness of those elevations and depths, the cor rectness with which the hard part of the earth has assumed the spheroidal form, and the absence of any particular preponder ance either of land or of water at the equator as compared with the poles, have induced most physicists to suppose, either that the interior of the earth is now fluid, or that it was fluid when the mountains took their present forms. This fluidity may be very imperfect; it may be mere viscidity; it may even be little more than that degree of yielding which (as is well known to miners) shows itself by changes in the floors of subterraneous chambers at a great depth when their width exceeds 20 or 30 feet; and this yielding may be sufficient for my present explanation. However, in order to present my ideas in the clearest form, I will suppose the interior to be perfectly fluid. A
Figure 2. Airy’s diagrams to illustrate non-isostatic and root-supported plateau. 44 D evelopment of Idea of Isostasy In the accompanying diagram, fig. 1 [in the present text, Figure 2, a], suppose the outer circle, as far as it is complete, to represent the spheroidal surface of the earth, conceived to be free from basins or mountains except in one place; and suppose the prominence in the upper part to represent a table-land, 100 miles broad in its smaller horizontal dimension, and two miles high. And suppose the inner circle to represent the concentric spheroid al inner surface of the earth’s crust, that inner spheroid being filled with a fluid of greater density than the crust, which, to avoid circumlocution, I will call lava. To fix our ideas, suppose the thickness of the crust to be ten miles through the greater part of the circumference, and therefore twelve miles at the place of the table-land. Now I say, that this state of things is impossible; the weight of the table-land would break the crust through its whole depth from the top of the table-land to the surface of the lava, and either the whole or only the middle part would sink into the lava. In order to prove this, conceive the rocks to be separated by vertical fissures [in Figure 2a, indicated by short, radial lines]; conceive the fissures to be opened as they would be by a sinking of the middle of the mass, the two halves turning upon their lower points of connexion with the rest of the crust, as on hinges; and investigate the measure of the force of cohesion at the fis sures, which is necessary to prevent the middle from sinking. Let C be the measure of cohesion; C being the height, in miles, of a column of rock which the cohesion would support. The weight which tends to force either half of the table-land down wards, is the weight of that part of it which is above the general level, or is represented by 50 X 2. Its momentum is 50 X 2 X 25 = 2,500. The momenta of the “couples,” produced at the two extremities of one half, by the cohesions of the opening sur faces and the corresponding thrusts of the angular points which remain in contact, are respectively C X 12 X 6 and C X 10 X 5; their sum is C X 122. Equating this with the former, C = 20 nearly; that is, the cohesion must be such as would support a hanging column of rock twenty miles long. I need not say that there is no such thing in nature. If, instead of supposing the crust ten miles thick, we had sup posed it 100 miles thick, the necessary value for cohesion would have been reduced to 1 /5th of a mile nearly. This small value would have been as fatal to the supposition as the other. Every D evelopment oe Idea of Isostasy 45 rock has mechanical clefts through it, or has mineralogical veins less closely connected with it than its particles are among them selves; and these render the cohesion of the firmest rock, when considered in reference to large masses, absolutely insignifi cant. . . . We must therefore give up the supposition that the state of things below a table-land of any great magnitude can be repre sented by such a diagram as fig. 1 [here Figure 2, a]. And we may now inquire what the state of things really must be. The impossibility of the existence of the state represented in fig. 1 has arisen from the want of a sufficient support of the table land from below. Yet the table-land does exist in its elevation, and therefore it is supported from below. What can the nature of its support be? I conceive that there can be no other support than that arising from the downward projection of a portion of the earth’s light crust into the dense lava; the horizontal extent of that projection corresponding rudely with the horizontal extent of the table land, and the depth of its projection downwards being such that the increased power of floatation thus gained is roughly equal to the increase of weight above from the prominence of the table land. It appears to me that the state of the earth’s crust lying upon the lava may be compared with perfect correctness to the state of a raft of timber floating upon the water; in which, if we remark one log whose upper surface floats much higher than the upper surfaces of the others, we are certain that its lower surface lies deeper in the water than the lower surfaces of the others. This state of things then will be represented by fig. 2 [here Figure 2, b]. Adopting this as the true representation of the arrangement of masses beneath the table-land, let us consider what will be its effect in disturbing the direction of gravity at different points in its proximity. It will be remarked that the disturbance depends on two actions; the positive attraction pro duced by the elevated table-land; and the diminution of attrac tion, or negative attraction, produced by the substitution of a certain volume of light crust (in the lower projection) for heavy lava. The diminution of attractive matter below, produced by the substitution of light crust for heavy lava, will be sensibly equal to the increase of attractive matter above. The difference of the negative attraction of one and the positive attraction of the 46 D evelopment of Idea of Isostasy other, as estimated in the direction of a line perpendicular to that joining the centres of attraction of the two masses (or as esti mated in a horizontal line), will be proportional to the difference of the inverse cubes of the distances of the attracted point from the two masses. Suppose then that the point C is at a great distance, where nevertheless the positive attraction of the mass A, considered alone, would have produced a very sensible effect on the apparent astronomical latitude, as ten seconds. The effect of the negative attraction of B will be 10" X CA3 / CB3; and the whole effect will be 10" X (CB3 — CA3) / CB3, which probably will be quite insensible. But suppose that the point D is at a much smaller distance, where the positive attraction of the mass A would have produced the effect n". The whole effect, by the same formula, will be n" X (DB3 - DA3) / DB3, or n" X (1 - DA3/DB3)\ and as in this case the fraction DA/DB is not very nearly equal to 1, there may be a considerable disturbing attraction. But even here, and however near to the mountains the station D may be, the real disturbing attraction will be less than that found by computing the attraction of the table-land alone. The general conclusion then is this. In all cases, the real dis turbance will be less than that found by computing the effect of the mountains, on the law of gravitation. Near to the elevated country, the part which is to be subtracted from the computed effect is a small proportion of the whole. At a distance from the elevated country, the part which is to be subtracted is so nearly equal to the whole, that the remainder may be neglected as in significant, even in cases where the attraction of the elevated country itself would be considerable. But in our ignorance of the depth at which the downward immersion of the projecting crust into the lava takes place, we cannot give greater precision to the statement. In all the latter inferences, it is supposed that the crust is floating in a state of equilibrium. But in our entire ignorance of the modus operandi of the forces which have raised submarine strata to the tops of the high mountains, we cannot insist on this as absolutely true. We know (from the reasoning above) that it will be so to the limits of breakage of the table-lands; but within those limits there may be some range of the conditions either way. It is quite as possible that the immersion of the lower projection D evelopment of Idea of Isostasy 47 in the lava may be too great, as that the elevation may be too great; and in the former of these cases, the attraction on the dis tant stations would be negative. Again reverting to the condition of breakage of the table-lands, as dominating through the whole of this reasoning, it will be seen that it does not apply in regard to such computations as that of the attraction of Schehallien and the like [mountains of small area]. It applies only to the computation of the attractions of high tracts of very great horizontal extent, such as those to the north of India.8 Thus by his root hypothesis Airy offered an explanation of the stable support of mountain chains, wide table-lands, and whole continents. Each tends to be completely floated by a corresponding root or downward projection of rock which has density smaller than that of average rock at and near the earth’s surface. However, he did not regard this support as necessarily perfect, even for highlands of consid erable breadth. He saw clearly that individual mountains are largely held up by the strength of the rocks composing them and their immediate surroundings; that the compensa tion for their heights is regional and not purely local. It is important also to observe what Airy did not mean when he launched his hypothesis. For him “crust” did not mean a true crust, literally conceived as a chilled and there fore crystallized, strong earth-shell, resting directly on a liquid, strengthless interior. His “lava” is not necessarily a true liquid, incapable of resisting small stresses indefinitely. He assumed the mean density of a projecting table-land to equal the mean density of the “crust,” which, however, he did not suppose to be itself uniform. He did not say how the “roots” were developed; for him this was a mystery. He did not suppose the temperature of the rock of the “crust” in any part to remain constant through geological time. In other words, his statement does not exclude ther mal attenuation as a supplementary condition for the height of table-land or mountainous mass. If Airy had 48 D evelopment oe Idea of Isostasy learned the facts now known about mountain-building, he would almost certainly have combined his “root” idea with that of thermal expansion and consequent change of topo graphic relief without change of mass. This type of dynamic attenuation was in the mind of Boscovich, and it was later to be more or less emphasized by Babbage, Herschel, and Pratt. Yet geologists, who can hardly fail to be still more impressed with the postulate of roots, will doubtless agree with those geodesists and geophysicists who attribute to Airy the first clear and relatively full statement of the isostatic hypo thesis. The contrast of the two kinds of compensation is suggested by Figures 3 and 4. The first of these drawings is a modified form of Bowie’s
PYRITE ANTI- ZINC MONY 1 RON T N SILVER COPPER LEAD 10.5 7.1 5.1 6.7 7.8 7.3 8.9 11.4 :------= MERCURY
F igure 3. Metal columns illustrating the Pratt-Hayford type of isostatic com pensation. The isopiestic level is at the base of each column. Figure 2 in Special Publication 99 of the United States Coast and Geodetic Survey (1924). There are shown columns of
—— 8.9 N 1 c K E L 8.9 -- ~ " ------— 8.9 ------_ — ------TZ__ ------M_ E___4 C U R Y 13.6------
F igure 4. Metal columns illustrating the Airy type of isostatic compensation. The isopiestic level is at the base of the longest column. metals with different densities but of equal mass. All the columns are free to move separately in the vertical direction, D evelopment of Idea of Isostasy 49 yet the base of each, when in equilibrium with the surround ing mercury, is on the same level as the base of every other column. This level interface between the solids and the liquid mercury represents the level of compensation for the “topography” above the mercury; the columns are in isos tasy of the Pratt type. Figure 4 portrays columns of nickel with density of 8.9, stably floating in mercury with density of 13.6. The pro jection above the liquid is in direct proportion to the relative degrees of immersion of the separate columns. Each column has its buoying “root,” analogous to the root of Airy’s hypothesis. Closer analogies are indicated in sections A and B of Figure 5, where the columns in the actual, though simplified,
Figure 5. Sections illustrating the Pratt-Hayford (A), Airy (B), and Heiskanen (C) types of isostatic compensation. earth have heights and densities matching the requirements of the Pratt and Airy kinds of compensation. The topog raphy compensated is the same in the two cases. Section C contains the Airy idea, but assumes increase of density in each rock column and also in the material that buoys up the columns. This third type of compensation has been emphasized by Heiskanen and will be referred to under his name. See p. 122. The levels of uniform pressure, or “isopiestic levels,” in the three systems are respectively 112.7, 60, and 74 kilometers below sea level. 50 D evelopment of Idea of Isostasy The Pratt and Airy explanations of the deflection residuals at Indian stations naturally prompted a test with the gravity pendulum, just as Bouguer (albeit with an imperfect instru ment) had tried to check the residuals alongside the Andes. Accordingly, from 1865 to 1871, Basevi measured the force of gravity at many points in India and proved it to be “very much less on the summit of the highly elevated Himalayan table lands than can be accounted for otherwise than by a deficiency of matter below; secondly, that it increases as the ocean is approached, and is greater on islands than can be accounted for otherwise than by an excess of matter below.”9 HALL In 1859, after many years of patient field work, James Hall gave the first geological proof that in principle Herschel was right when he theoretically pictured isostatic adjustment for the transfer of load during secular erosion at the earth’s surface. Hall discovered the shallow-water character of the sediments constituting the Appalachian mountains, as shown by the recurrence of ripple-marks and remains of plants deep in the stratified series of beds. From this observation he argued a “yielding of the earth’s crust” beneath the load of accumulating sediments, and a gradual subsidence of that crust as a consequence. Although he did not say it ex plicitly, his express acceptance of Herschel’s theory implies that Hall assumed outward horizontal flow of subcrustal material as an accompaniment of the sinking of sediment and sedimentary floor.10 JAMIESON In 1865, Jamieson—using geological observations quite different from Hall’s—also showed a way of proving the great sensitiveness of the earth’s body to extensive loads placed on the surface, even if the pressure per unit of area is relatively small. His statement was brief but clear. The D evelopment of Idea of Isostasy 51 weight of each major icecap of Pleistocene time depressed, basined, the rocky surface beneath, and the melting of a cap has been followed by the slow recoil of the rocky surface. He saw that the basining involved horizontal, outward flow in the subglacial sector and not merely an elastic, volumetric compression of the sector. His views were more definitely stated seventeen years later. Then he argued against the views of Adhemar and Croll, that the earth is too rigid to yield plastically at all under the weight of a great icecap; that the center of gravity of the globe must be displaced toward the middle point of the cap; and that the sea level is correspondingly raised on the flanks of the ice and lowered in the opposite hemisphere. Jamieson asked: Would not the centre of gravity of the earth be more likely to pull the cap down than the cap to shift the centre of gravity? The earth would require to be a very rigid body indeed to sustain such a weight for thousands of years without yielding. . . . It appears more likely that the position of the surface [of the earth] is in a state of delicate equilibrium, and that any considerable transference of pressure will cause a re-adjustment of levels. . . . It seems likely that there might be not only a slight sinking of the ice-covered tract, but likewise a tendency to bulge up in the region which lay immediately beyond this area of depression; just as we sometimes see in the advance of a railway embank ment, which not only depresses the soil beneath it, but also causes the ground to swell up farther off.11 (See chapter 10.) DUTTON In 1889, C. E. Dutton introduced the word “isostasy” in a classic paper from which a significant passage may be quoted: If the earth were composed of homogeneous matter its normal figure of equilibrium without strain would be a true spheroid of revolution; but if heterogeneous, if some parts were denser or lighter than others, its normal figure would no longer be spher 52 D evelopment of Idea of Isostasy oidal. Where the lighter matter was accumulated there would be a tendency to bulge, and where the denser matter existed there would be a tendency to flatten or depress the surface. For this condition of equilibrium of figure, to which gravitation tends to reduce a planetary body, irrespective of whether it be homo geneous or not, I propose the name isostasy [from the Greek isostasios, meaning “in equipoise with”; compare isos, equal, and statikos, stable]. I would have preferred the word isobary, but it is preoccupied. We may also use the corresponding ad jective, isostatic. An isostatic earth, composed of homogeneous matter and without rotation, would be truly spherical. If slowly rotating it would be a spheroid of two axes. If rotating rapidly within a certain limit, it might be a spheroid of three axes. But if the earth be not homogeneous—if some portions near the surface are lighter than others—then the isostatic figure is no longer a sphere or spheroid of revolution, but a deformed fig ure, bulged where the matter is light and depressed where it is heavy. The question which I propose is: How nearly does the earth’s figure approach to isostasy?* The very form of his question shows that Dutton did not believe isostatic balance to be absolutely perfect. For him isostasy was a tendency toward an ideal condition—a condi tion never actually attained. He was aware of the lag in the balancing adjustments for shifts of load on the surface of the planet, even where such disturbance simultaneously affected an area of continental proportions. Moreover, he thought it “extremely probable that small or narrow ridges are not isostatic, with respect to the country round about them. Some volcanic mountains may be expected to be non-isostatic, especially isolated volcanic piles.” On the other hand, he did estimate the minimum size of a load that must initiate isostatic adjustment; the mass involved would be equivalent to “a single mountain platform, less than 100 * C. E. Dutton, Bull. Phil. Soc. Washington, vol. 11, 1889, p. 51 (reprinted in Jour. Washington Acad. Sci., vol. 15, 1925, p. 359; and again in Bull. 78 of the Nat. Research Council on “The Figure of the Earth,” 1931, p. 203). Presumably “earth’s figure” of the quotation meant the shape of the solid part of the earth, not the geoid, ellipsoid, or spheroid of the geodesists. D evelopment oe Idea of Isostasy 53 miles in length, from 20 to 40 miles wide, and from 2,500 to 3,500 feet mean altitude above the surrounding lowlands.” While Dutton emphasized the horizontal variation of density in the rock near the earth’s surface as the chief cause of topographic relief, he suggested no specific figure for the thickness of the layer containing this variation of density. However, his explanation of mountain-building, outlined toward the end of his paper, implies that he assumed the underlying shell, where isostatic flow takes place, to begin only a few miles below the surface. GILBERT A few months after Dutton made his address, Gilbert, another geologist, supported Dutton’s conception in princi ple, writing: It is believed that the following theorem or working hypothesis is worthy of consideration and of comparison with additional facts: mountains, mountain ranges, and valleys of magnitude equivalent to mountains, exist generally in virtue of the rigidity of the earth’s crust; continents, continental plateaus, and oceanic basins exist in virtue of isostatic equilibrium in a crust hetero geneous as to density.12 Since 1889, many quantitative tests of the isostatic prin ciple have been made. Those founded on geodetic measure ments have become practical and valuable by arbitrarily assuming perfect hydrostatic equilibrium at depth greater than that of a level not far below the surface of the earth. The depth of this level is the assumed depth of isostatic com pensation for the topography of the globe. Below it is an infinitely weak earth-shell, and above it an elastically com petent shell—that is, one able to bear shearing-stress for an indefinitely long time. Above the depth of compensation, high land is held up, not only by the strength of the rock just below the surface, but also by defect of density in that rock; each wide basin remains a basin because the underlying 54 D evelopment of Idea of Isostasy rock has density greater than the average density of rock at the same range of levels near the surface. HELMERT; SCHWEYDAR The great German authority on geodetic theory, F. R. Helmert, devised a special method of testing the idea of isostasy. He considered how adjacent, balanced columns of differing densities, and extending from top to bottom of the layer of compensation, affect gravity at the top of each column. Evidently on the long column the value of this force (y0), normal for the given latitude and longitude, is increased by the vertical component of attraction exerted by the lower-lying, denser rock that constitutes the shorter column. Normal gravity on the shorter column should in an analogous way be modified, but the disturbance would have the opposite sign. According to the isostatic hypothe sis, such horizontal variation of density is represented on a large scale where continents and deep oceans meet. Within such a zone the difference between y0 and observed gravity (go); or (go ~ T o )- is a function of the depth of compensa tion. Hence Helmert reasoned that, if the compensation be supposed uniformly distributed with respect to depth, it is possible to secure an estimate of the depth of compensation by studying actual values of gravity along profiles across the marginal zones of the continents.13 Helmert selected three groups of stations: group I (14 stations), on shores where the average continental slope is 1 : 28 and the average distance (a) of station from the fall- off of the slope is 27 kilometers; group II (13 stations), where the continental slope was decidedly less than 1 : 28; and group III (24 stations), with a distance considerably greater than 27 kilometers. Column 3 of Table 3 gives the mean values of a; column 4, the observed mean “anomalies” (go ~ T o); columns 5 and 6, the respective “disturbances” of normal gravity, computed after arbitrarily assuming the D evelopment of Idea of Isostasy 55 depth of ocean at the foot of each continental slope to be 4,000 meters and assuming the depth of compensation to be, first, 128 kilometers and, second, 64 kilometers.
T able 3 OBSERVED AND THEORETICAL GRAVITY AT CONTINENTAL SHORES (milligals)
Computed (g0 — To), Number Observed compensation complete Group of at depth of: stations (km) (milligals)(*o “ T0> 128 km 64 km i 14 27 +51 +57 +36 ii 13 32 +39 +41 +23 h i 24 115 + 26 +27 +24 Average for 3 groups +36 +40 +24
From these results Helmert estimated the most probable depth of compensation to be 118 kilometers. Although the possible error was recognized as perhaps 20 per cent, the estimate means an order of magnitude like that which had been reached by Hayford by a totally different method, in volving study of deflections of the vertical, a method to be described in the next chapter. At Helmert’s request, O. Meissner calculated the changes of “anomaly” (difference between observed and theoretical gravity) across the edge of a continent, as demanded by the Pratt type of compensation, the continental surface being supposed to be uniformly at sea level, the depth of compen sation at 100 kilometers, the continental slope at 1° 8', the depth of the ocean at and outside the foot of the continental slope being 4,000 meters, and the density of the rock at sea level being 2.73. The results of the computations are ex pressed graphically in the broken-line curve of Figure 6. The positive anomaly is greatest at the shore line. Schweydar made a similar comparison, all assumptions 56 D evelopment of Idea of Isostasy being the same except that the Airy type of compensation was postulated, with sea-level thickness of the sial or “crust” taken at 204 kilometers. This relatively great thickness was taken in order to bring the calculated anomalies on land
+60 -
Figure 6. Helmert-Meissner and Schweydar curves of coast anomaly, based re spectively on the Pratt-Hayford and Airy types of isostatic compensation. into approximate equality with those actually listed as “ob served” by Helmert. Schweydar found a great algebraic decrease of the anomalies from the coast seaward, as com pared with their values deduced on the Pratt hypothesis. (See the continuous curve of Figure 6.) In spite of this re sult, which is correlated with a difference of only 0.034 be tween the densities of sial and sima, the Airy curve, like the Pratt curve, illustrates a principle—that considerable anom alies of gravity may exist across strong discontinuities of topography, even with perfect isostatic support of the lithosphere.14 SUGGESTIONS REGARDING ISOSTATIC COMPENSATION The history of the isostatic idea will be continued in the following chapters, but it may be useful to interpolate at D evelopment of Idea of Isostasy 57 this point a brief review of all the principal suggestions made before the year 1940 about the nature of isostatic compensa tion of the earth’s topography. Since the material more than a few kilometers below the earth’s surface is inaccessible, the variation of density along the hidden levels is not easily found. Some important clues are supplied by seismology and structural geology, but more detailed information comes from the gravity field. Rela tively superficial masses of rock with abnormal density, high or low, are discoverable with the Eotvos balance, which measures the abnormal curvatures of levels; however, by this method of investigation the depth and volume of each disturbing mass can not be exactly determined. Two more telling ways of discerning the horizontal variation of density at depths of tens of kilometers will be described in the next five chapters. Neither method can give a direct result, untroubled by theory. The observed gravity field agrees with any one of an infinite number of conceivable arrangements of density in depth. Fortunately, it has already become clear that the problem is not so intractable as this statement would seem to imply. The possibilities are of infinite number, but they are nevertheless within limits so close together that the range of uncertainty can be small. The limits are set by several well-known facts and sets of facts. Among these are: the mean density of the earth; its moment of inertia, from which a considerable increase of density with increase of depth is clearly deducible; data from physical geology; the particularly valuable observations of the detective seis mologists ; and the general law that, because of -the limited strength of all known rocks, the major reliefs of the globe imply buoyant support for them, nearly perfect hydrostatic conditions at depth, and corresponding distribution of den sities along the levels deep underground. Considering all these helps to thought, geophysicists do 58 D evelopment of Idea of Isostasy not regard the problem as hopelessly elusive, but have at tacked it on the basis of trial and error. Their results have proved to be highly valuable, though many questions of detail are still open. 1. According to one hypothesis, it is assumed that there is no compensation for topography; that, from sea level upward, each block of high land represents an extra load on the earth’s body; and that the oceanic sectors are out of balance in the opposite sense, the measure of the departure from balance being practically the difference of mass be tween sea water and the rock projecting above the sea bot tom. This hypothesis is certainly erroneous; yet we are to see that upon it can be based computations that prove the rule of close isostasy as between continent and ocean and between great mountain chains and the surrounding lands. 2. At the other extreme of conceivable hypotheses is one which assumes that mountain or continent is compensated for at zero depth, as if mountain or continent above sea level were like an empty eggshell, with no mass whatever. This apparently absurd idea also has practical value, for it gives the best basis for calculating the external field of gravity for the earth. Such calculation is indirectly important in the problem of isostasy. 3. As yet the most elaborate studies of the relation be tween gravity and the implications of isostasy have premised uniform compensation in depth, the depth of compensation being also uniform and only a small fraction of the earth’s radius. This third hypothesis, erected partly for mathe matical convenience, has several variants. According to one of them the compensation is supposed to be perfectly local, each column of rock immediately under an infinitesimal area of high ground or low ground being balanced because of appropriate differences of density of the material in the thin layer of compensation. The pressure at the depth of com pensation is therefore hydrostatic. D evelopment of Idea of Isostasy 59 The second variant is phrased in terms of the obvious fact that the rock of the layer of compensation offers practically permanent resistance to forces of vertical shear, the com pensation being necessarily regional. In other words, the compensation for any topographic irregularity is supposed to be spread horizontally in all directions from the center of this topographic form, though to a limited distance. In practice, the horizontal area covered by such regional com pensation for the topography around each gravity station is arbitrarily assumed to be a circle with its center at the station. The principle of regional compensation is illustrated in Figure 7, where the load is seen to have depressed the litho-
F igure 7. One kind of regional compensation for topography. sphere, originally level, and, because of the finite viscosity of the asthenosphere as well as the strength of the litho sphere, to have developed a low bulge around the depressed area. The amount of the bulge expected in the actual earth is indicated, though in exaggerated degree, by the slight thickening of the line under the surface of the bulged zone. Another variant of the third hypothesis assumes the com pensation to be uniform in depth, but the depth of compen sation to be variable from topographic province to topo graphic province. 4. According to a fourth group of hypotheses, the com pensation is concentrated in one or more comparatively thin layers, each with its top at moderate depth. That condi tion is implicit in Airy’s idea of “roots.” The root of moun- 60 D evelopment of Idea of Isostasy tain range or continent is irregular, but for ease of mathe matical treatment a root may be regarded as divided into a small number of parts, each part ending below at a smooth, horizontal interface with the supporting material. How ever, here as in the case of the Pratt type, a purely local com pensation is mechanically impossible, and the effects of roots on the plumb line and gravimeter may be closely estimated, if the compensation be regarded as complete along some
Geoid
SIMA Local Compensation
SIMA
Figure 8. Regional compensation according to the Airy hypothesis. such surface as that represented by the line labeled “re gional compensation” in Figure 8. 5. By a more complex hypothesis the compensation is assumed to be partly by roots and partly by what may be called “anti-roots.” See Figure 9, with sections of sial- bearing segments of a true crust of the earth (surfaces at 800 and 3,000 meters above sea level). These columns are balanced by ocean-bearing segments (water 4,200 meters deep). All columns rest on an earth-shell supposed to be too hot to crystallize. The corresponding gradients of tern- D evelopment of Idea of Isostasy 61 perature are supposed to differ, primarily because of differ ing rates of radioactive heating in sial and sima. Thus the continent has its vitreous anti-root with relatively low dens ity, and the support of the mountain chain is, in addition,
Figure 9. Illustrating the hypothesis that part of the isostatic compensation is supplied by “anti-roots.” The isopiestic level is at the base of the sub-oceanic column. guaranteed by the special anti-root of the mountain chain as well as by the sialic root. The isopiestic level is put at 77 kilometers below sea level, but this and other numerical values entered in the section are no better than rough esti mates of the quantities involved. The anti-root kind of compensation is briefly described in the writer’s books en titled “Igneous Rocks and the Depths of the Earth” (New York, 1933) and “Architecture of the Earth” (New York, 1938). Figure 9 was drawn with special reference to the facts of dynamical geology, as recorded, since the late Pre-Cambrian. In principle the diagram may represent the average condi tions during those half-billion years, though the average thickness of the “gabbroic” layer was probably smaller than it is shown. In chapter 1 (section on discontinuities), we saw that the diagram should be somewhat modified to allow for new data bearing on the problem of the nature of the earth-shells at the present time. Nevertheless, as it stands, Figure 9 serves to illustrate the principle of the anti-root. 62 D evelopment of Idea of Isostasy 6. Finally, the compensation may be explained by a com bination of all five of the above-listed hypotheses. This idea seems to furnish the most probable basis for under standing the earth’s relief, though, since there are so many variables, its quantitative discussion is likely to baffle the mathematician.* Barrell published an instructive diagram showing how different types of isostatic compensation may satisfy about equally well the data regarding deflections of the plumb line and data regarding the intensity of gravity. This drawing is reproduced in Figure 10, where the shaded
Figure 10. Alternative distributions of isostatic compensation. areas represent distributions of the compensation that are alternative with the Pratt type (area B), the depth of com pensation being here taken at 113.7 kilometers or 70.7 miles. For a measuring instrument at a considerable distance from the column, the effective center of gravity of the compensa tion is halfway down the column, or at the depth of 35.3 miles. Area A represents compensation confined to a stra tum 10 miles thick; its gravitational effects are almost iden * Different dynamic processes lead to isostatic compensation. On the one hand, it may be accomplished by flow of matter. For example, erosion removes load from a mountainous belt until the lithosphere yields to the stresses so developed. Then correcting flow of the asthenospheric material takes place. On the other hand, compensation for a topographic relief may be essentially due to thermal expansion or contraction of the underlying part of the lithosphere, without any lateral flow of matter into, or from, the earth-sector involved. D evelopment of Idea of Isostasy 63 tical with those of case B, if the center of gravity of the A area is 32 miles down. Area C represents compensation with maximum at sea level and decreasing uniformly to a limiting depth of 109 miles; the corresponding center of gravity of compensation is 36.3 miles down. Area D has the compensation decreasing at a variable rate to the depth of 178.6 miles; the center of gravity of compensation is now 37.0 miles down.15 In view of the great range of possible choices for the dis tribution of underground masses capable of explaining the earth’s gravity field, the worker with the gravitational method of diagnosing the depths needs all the outside help he can get. Heiskanen has emphasized this conclusion: It looks as if the investigation of the isostatic doctrine is at a turning-point. Hitherto the geodesists, seismologists, and geol ogists have worked too independently, each group failing to pay sufficient attention to results won in the two closely associated fields of research. For example, the measurements of gravity have been made at stations whose locations have been chosen without sufficient regard to tectonic and other geological condi tions. Each group of investigators has, as it were, surveyed the processes operating below the earth’s surface through its own, more or less distorting lens. The geodesist has assumed the facts to be different from those deduced by the seismologist, and both view the facts differently from the geologist. Hence there has been much misunderstanding, and the development of sound conclusions has been delayed.16
R efer en ces 1. C. Maire and R. J. Boscovich, “Voyage Astronomique et Geographique,” Paris, 1770, p. 463—translation of “De Litteraria expedilione per pontificam ditionem ad dimetiendos duos meridiani gradus,” Rome, 1755. 2. C. Babbage, Ninth Bridgewater Treatise, second edition, 1838, p. 213; Proc. Geol. Soc. London, vol. 12, 1847, p. 368; A. Knopf, “Bibliography of Isostasy,” published in mimeo graphed form by the National Research Council, Washing 64 D evelopment of Idea of Isostasy ton, 1924, p. 15; C. R. Longwell, Amer. Jour. Science, vol. 16, 1928, p. 451. 3. F. Petit, Comptes Rendus, Acad. Sci., Paris, vol. 29, 1849, p. 730. 4. J. H. Pratt, Phil. Trans. Roy. Soc. London, vol. 145, 1855, pp. 53, 55. 5. J. H. Pratt, Phil. Trans. Roy. Soc. London, vol. 149, 1859, pp. 747, 763. 6. J. H. Pratt, Phil. Trans. Roy. Soc. London, vol. 149, 1859, p. 779; vol. 151, 1861, pp. 579, 594. 7. G. B. Airy, Phil. Trans. Roy. Soc. London, vol. 145, 1855, p. 101-4. 8. G. B. Airy, op. cit., pp. 101-4. 9. See J. T. Walker, Nature, vol. 32, 1885, p. 486. 10. James Hall, “Geology of New York State,” vol. 3, 1859, p. 69; Canadian Journal, 1860, p. 542. 11. T. F. Jamieson, Quart. Jour. Geol. Soc. London, vol. 21, 1865, p. 178; Geol. Mag., vol. 9, 1882, sep., pp. 4, 6, 13. 12. G. K. Gilbert, Bull. Geol. Soc. America, vol. 1, 1890, p. 23. 13. F. R. Helmert, Sitzungsber. preuss. Akad. Wiss., 1909, p. 1192. 14. See W. Schweydar, Zeit. f. Geophysik, vol. 2, 1926, p. 148. 15. J. Barrell, Amer. Jour. Science, vol. 48, 1919, p. 325. 16. W. Heiskanen, Gerlands Beilraege zur Geophysik, vol. 36, 1932, p. 201. 3 TESTING ISOSTASY WITH THE PLUMB LINE
By the year 1894, geodesists were equipped with apparatus for systematic attack on a question which had become more and more pressing during a century of research: How much does the actual degree of isostasy affect calculation of the true figure of the earth? The attempts to answer this ques tion have incidentally provided a valuable test of the iso static principle itself. Two methods of investigation have been developed. One of these is based on study of the de flections of the vertical or plumb line at geodetic stations; the other, on measurements of the force of gravity at sta tions of known heights, latitudes, and longitudes. The first method will now be considered, and later the second. On account of their great importance, each will be described in considerable detail. Many statements already made re garding fact, hypothesis, and argument will be repeated, but such repetition may be helpful in a field of thought so com plicated. DEFLECTIONS OF THE VERTICAL Every projecting mass of land attracts a plumb bob ac cording to the law of gravitation. Every hollow in the sur face of the solid earth represents failure of similarly hori zontal attraction. At any point the plumb line responds faithfully to all such positive and negative calls. It is also affected by the positive or negative attractions correspond- 65 66 Testing Isostasy with the Plumb Line ing to the densities of local masses of rock where these densi ties are respectively greater or less than that of normal rock at the same levels and distances. Thus the direction of the plumb line or vertical is affected by pulls of all four kinds. The horizontal component of each pull deflects the plumb line. The principle involved is illustrated by Figure 11, a
Figure 11. Effect of the attraction of a mountain on the plumb line. section through a mountain. At stations A and B the ver tical is represented by the lines AM and BM7, respectively. If the mountainous mass were absent, the earth being per fectly smooth and of uniform density along each level from surface to center, the corresponding verticals would be dif ferent, in the sense of AO and BO7. The total deflection is thus the sum of the angles MAO and M7B07. The effect of all attractions on the plumb bob at any sta tion can be evaluated only after time-consuming computa tions have been made. Just as clearly, a large number of stations, widely distributed, have to be occupied before an adequate basis can be laid for testing isostasy by comparing observed and theoretical deflections. The job is not one for an individual. It requires the resources of a great Gov ernment bureau, and in fact it was first undertaken on a large scale by the United States Coast and Geodetic Survey. Testing Isostasy with the Plumb Line 67 HAYFORD’S FIRST INVESTIGATION In the year 1906, the Survey had occupied enough trian gulation stations to give its Inspector of Geodetic Work, J. F. Hayford, data warranting an attempt to learn how far the topography of a region as large as the United States is isostatically compensated. The results are to be found in two quarto volumes published by the Survey: “The Figure of the Earth and Isostasy” (1909) and “Supplementary Investigation in 1909 of the Figure of the Earth and Isostasy” (1910). Hayford showed that the multitudes of observed deflec tions of the vertical can be understood only by assuming a close approach to isostasy, a nearly perfect balancing of part against part throughout the broad territory, and balancing of the whole by the Pacific and Atlantic segments of a super ficial earth-shell. His argument will be summarized and illustrated, many essential statements appearing in his own words.* The investigations were founded on the use of theodolite and spirit level, which fixed the geodetic latitudes, longi tudes, azimuths, and heights of the stations in networks of primary triangulation. The operation involves measure ment of exceedingly minute vertical angles; in general any errors made during these particular measurements are negli gible when observed deflections of the vertical from its theoretical positions at the different stations are computed. In the nature of the case, the values found for the geodetic elements had to be based on a selected “figure of the earth,” a selected ellipsoid of reference, and also on the assumption that some one station lies at a fixed point on that ellipsoid. Clarke’s ellipsoid, proposed in the year 1866 (see Table 1), was chosen. The station selected for the fixed point was * A brief but clear summary of the argument is contained in one of J. Barrell’s posthumous papers (Amer. Jour. Science, vol. 48, 1919, p. 283). 68 T esting Isostasy with the Plumb Line that at Meades Ranch in Kansas, not far from the geo graphical center of the United States. For this station the following elements were assumed: latitude, 39° 13' 26".686; longitude, 98° 32' 30".506; azimuth of the line from Meades Ranch to the triangulation station at Waldo, 75° 28' 14".52. Thus the networks of stations were definitely orientated on the Clarke ellipsoid of reference, and Meades Ranch became the United States Standard Datum. After the geodetic latitude and longitude of any station other than that at Meades Ranch were found by triangula tion, the line normal to the Clarke ellipsoid at that station was fixed in relation to the stars and the celestial sphere. At the same station the astronomical latitude and longitude were directly measured by observations on the stars, with the zenith telescope and astronomical transit. This second operation gave the actual direction of the plumb line, the actual vertical, or the position of the zenith on the celestial sphere. At nearly every station in the United States the direction of the normal to the ellipsoid of reference was found to differ from the direction of the plumb line or zenith, by an amount greater than could be explained by error in observing and computation. This difference is the “deflection of the plumb line or vertical.” In his main investigation (1909), Hayford used determina tions of astronomic latitude at 265 stations; of astronomic longitudes at 79 stations; and of 163 azimuths. For each latitude station the component of the deflection that lay in the meridian was found. For each of 231 stations the com ponent of the deflection that lay in the prime vertical—that is, in the great-circle plane passing through the stations and cutting the meridional plane at right angles—was calculated. Examples of the determined deflections of the vertical in the meridian are given in Table 4, where the second column gives for each station this difference between the geodetic Testing Isostasy with the Plumb Line 69 and astronomic latitudes. Here a plus sign means that the plumb line or vertical cuts the celestial sphere farther north than the zenith defined by the normal to the Clarke ellipsoid of reference. Column 2 of Table 5 gives examples of the analogous com puted deflections in the prime vertical. These were derived from observations of both longitude and azimuth. The plus sign means that the zenith defined by the plumb line is farther west on the celestial sphere than the corresponding zenith fixed by the line normal to the Clarke ellipsoid.
T able 4 DEFLECTIONS IN THE MERIDIAN (seconds of arc) 1 2 3 4 5 6 Computed deflection, with depth of Observed Topographic compensation at deflection deflection 162.2 km 120.9 km 113.7 km 33, Pioche -4.38 -33.47 -4.04 -3.22 -3.09 62, Wallace -0.10 -11.74 +0.09 +0.13 +0.13 113, Roslyn -2.24 -31.30 -0.77 -0.70 -0.34 136, Yard +4.59 -33.22 -3.05 -2.43 -2.35 218, Huron Mts + 10.50 -1.90 +3.02 +2.68 +2.60 238, Santa Barbara -18.38 -64.97 -14.91 -12.78 -12.35 254, Pt. Pinos +0.29 -50.71 -4.89 -3.30 -2.98
T able 5 DEFLECTIONS IN THE PRIME VERTICAL (seconds of arc)
1 2 3 4 5 6 Computed deflection, with depth of Observed Topographic compensation at deflection deflection 162.2 km 120.9 km 113.7 km 1, Point Arena + 16.98 + 104.63 +20.39 + 16.45 + 15.69 9, Mt. Hamilton + 10.05 +87.89 + 12.91 + 10.65 + 10.26 22, Verdi -4.05 +62.16 -0.42 -1.59 -1.78 64, Wallace -4.31 -21.26 -4.06 -3.02 -2.84 113, Roslyn -3.57 -44.31 -2.43 -1.77 -1.66 157, Cambridge + 1.34 -40.08 -2.66 -2.04 -1.95 194, Cleveland -0.23 -19.64 + 1.45 + 1.32 + 1.32 70 Testing Isostasy with the Plumb Line
T o po g r a ph ic D e f l e c t io n s . An early step toward find ing the reason or reasons why the observed deflections differ from the theoretical was taken by computing the horizontal attraction of the topography surrounding each station. With the help of a computing staff, Hayford set himself this heavy task. Success with it was seen to be assured if the needed maps be in hand, if the density of the rock underly ing the topography be known, and if a system of mensura tion be adopted that would give good results without a pro hibitive cost in time and labor. For the 1909 investigation, the topography out to the distance of 2,564 miles in all directions from each station was considered, the influence of the topography outside this circle being neglected. Inside the circle, 37 others, concen tric with it and drawn with radii ever increasing with dis tance from the station, were imagined to divide the topog raphy (subaerial and submarine) into 38 rings. Three considerations operated to fix upon the ring which has for its outside radius 4,126 kilometers (2,564 miles) as the largest ring to be taken into the computation of the topographic deflec tions : (a) In the next larger ring considerable areas would be in cluded for which our knowledge of the elevations is very limited, as, for example, the unexplored Arctic regions and the interior of South America, (b) The largest ring included in the com putation has a sufficiently great outer radius to insure that for stations in the extreme eastern part of the United States the ring reaches to the Pacific, and that for extreme western stations it reaches to the Atlantic. Hence the whole width of the continent is taken in by the computation. In the next larger ring, for any station, portions of each ocean would be included, and in general would tend to balance each other. Hence the total computed effect for each larger ring omitted will be in general considerably less than for each of the last few rings included in the computa tion. (c) The larger the ring considered the more nearly the computed topographic deflection corresponding to that ring tends to approach a constant value for the whole United States, and, therefore, the less serious is the effect of omitting said ring. (Report, p. 29.) Testing Isostasy with the Plumb Line 71 As a basis for calculating the topographic deflection in the meridian, Hayford used the following equation, which had been derived by Clarke: D = 12".44 h(S/A) (sin a' — sin a\) log„ (r'/Vi). (1) [Here] D is the meridian component of the deflection at the station produced by a mass of the surface material of the earth which is a stratum h statute miles thick, lying within a four-sided compartment limited by two radial lines drawn from the station and by two arcs of circles with their common center at the station and having the radii r' and n . a! and a\ are the angles between each of the two radial lines and the meridian. 5 is the mean surface density of the earth. A is the mean density of the earth as a whole. The constant 12".44 depends upon the supposition that for the present purpose the earth may be considered a sphere of which the radius is 6,370 kilometers, or 3,960 miles. The whole of the attracting stratum is assumed to be in the horizon of the station. (Report, p. 20.) Where D represents the prime-vertical component of the deflection, the same formula applies if the angles a ' and ai are measured from the prime vertical. Hayford continues: If the stratum considered within any compartment be that which is limited below at sea level and above at the actual irregular sur face of the earth, then with considerable accuracy the following statement, based upon the formula, may be made: For compart ments bounded by circles whose radii are in geometric progres sion, and by radial lines the sines of whose angles with a reference line are in arithmetic progression, the deflections produced at a station at the center of the circles, in a direction parallel to the reference line, are, for each compartment, proportional to the mean elevation of the land surface within this compartment. The use of this method of division into compartments makes the computation much shorter and more convenient than it would otherwise be. The statement that for such compartments the deflections produced are proportional to the mean elevations is subject to 72 Testing Isostasy with the Plumb Line three principal reservations affecting its accuracy. These reser vations refer—(a) To compartments so far from the station that the curvature of the earth’s surface must be considered. This matter has been attended to by increasing the radii of cer tain of the outer circles, as indicated on page 22. (b) To com partments near the station of which the mean surface lies so far above or below the station as to make a slope correction neces sary. The method of computing the slope correction is given under the appropriate heading later, (c) To compartments of which some part lies far above or far below the mean elevation for the compartment. This matter will be discussed later in connection with the other errors of computation. In some instances this third complication demanded special corrections to the results given by the standard formula. The mean density of the earth was assumed to be 5.576, which is one per cent too high; the mean density of the rock at and near the surface of the earth was assumed to be 2.67, which may be one per cent too low. Since r'/rx and (sin a! — sin di) may be taken at arbitrary values, those were adopted, for Rings 7 to 38 inclusive, which would facilitate computation: r' a t 1.426 and (sin a' — sin a-i) at 0.25. With these values the foregoing formula reduces to D = OTOOOIOOO ( h , in feet). As a result, then, of this particular selection of arbitrary con stants defining the limits of the compartments, the deflection produced at the station by the material lying above sea level in any compartment is, expressed in hundredths of seconds of arc, the same as the mean elevation of the surface within the com partment expressed in hundreds of feet. This particular selec tion of constants saved a large number of multiplications which would otherwise have been necessary. The outer radius of Ring 23 was arbitrarily taken at ex actly one statute mile. On account of the curvature of the earth, Rings 1 to 6 inclusive had, in the interest of greater accuracy, their radii increased beyond the lengths set by the ratio 1.426. Testing Isostasy with the Plumb Line 73 Table 6 gives the lengths of the different radii. In each ring there are sixteen compartments, four in each quadrant.
T able 6 RINGS FOR MENSURATION
Ring Outer radius Ring Outer radius Miles Kilometers Miles Kilometers i 2,564 4,126 20 2.899 4.665 2 1,757 2,828 21 2.033 3.272 3 1,219 1,962 22 1.426 2.295 4 850.8 1,369 23 1.000 1.609 5 595.2 957.9 24 .7013 1.129 6 416.8 670.8 25 .4918 .7915 7 292.2 470.3 26 .3449 .5551 8 204.9 329.8 27 .2419 .3893 9 143.7 231.3 28 .1696 .2729 10 100.77 162.27 29 .1190 .1915 11 70.67 113.73 30 .0834 .1342 12 49.56 79.76 31 .0585 .0941 13 34.75 55.92 32 .0410 .0660 14 24.37 39.22 33 .0288 .0463 IS 17.09 27.50 34 .0202 .0325 16 11.987 19.29 35 .0142 .0228 17 8.406 13.53 36 .0099 .0160 18 5.895 9.487 37 .0070 .0112 19 4.134 6.653 38 .0049 .0079 For compartments located in oceanic areas, 8 was given a value different from 2.67, the value assumed for land com partments. To treat the depths below mean sea level in the same manner as the land elevations above mean sea level, with only a change in the algebraic sign, would be equivalent to assuming the space between sea level and the ocean bottom to be void, whereas, in fact, it is filled with sea water having a density of 1.027. If the sea water were to increase in density from 1.027 to 2.67 (the mean surface density of the earth) by simply decreasing in volume and depth, without any horizontal transfer of material, and remaining in contact with the original sea bottom, the new depth of material would everywhere become .385 (1.027/2.67) of the former depth and the new surface would everywhere be .615 (= 1 — .385) below the original sea level. Hence, in the computation of topographic deflections, each ocean compart 74 Testing Isostasy with the Plumb Line ment has been considered as if it were a void from sea level down to a depth .615 of the actual mean depth of that compart ment. . . . For compartments which are partly oceanic areas and partly land areas especial care must be taken in estimating the mean elevation to keep in mind the negative sign . . . in connection with the water portion of the compartment. . . . In compartments containing fresh water lakes a process some what similar to that followed for ocean areas is necessary. Ac count must be taken of the fact that the density of the lake water is 1.000 and that the lake surface is at a certain known elevation above mean sea level. The foregoing formula for computing the total attraction of the rock that underlies a compartment is correct only where such attracting material lies in the horizon of the sta tion. In general, this is not the case; hence a “slope” correc tion has to be made. The formula for the correction is de rived on p. 34 of the memoir. The correction increases D, if the surface of the compartment is below the station and is not below sea level; and decreases D, if the surface of the compartment is above the station, or if the marine area in any compartment dominates in the calculation of the de flection due to that compartment. In the 496 computations of topographic deflections which have been made, appreciable slope corrections have been found in 43 computations. In each of these computations the slope correc tions were found to be appreciable for only a few compartments, and no correction exceeded 0",05 for any compartment. For each scale of map or chart to be used in the computations the circles and radial lines defining the limits of the compartments were drawn to the proper scale on a sheet of transparent cellu loid. Such a celluloid sheet, with compartment boundaries on it, has, for convenience, been called a “template”. . . . By the use of these transparent celluloid templates, the many circles and radial lines, fixing the limits of the compartments on a given map, were superposed on the map by the mere process of laying the template on the map in the proper position. The use of the templates saved a very considerable amount of labor which Testing Isostasy with the Plumb Line 75 would otherwise be necessary in drawing in many thousands of compartments on many hundreds of maps. It also left the maps without damage or defacement. (Report, pp. 23-4.) One style of template is illustrated in Figure 12, a slightly modified copy of Hayford’s Illustration No. 2. Here the distinguishing numbers are marked upon the sectors limited by radial lines. For a computation of the meridian component
Figure 12. Template used by Ilayford. of the topographic deflection, the reference line is pointed toward the north and the sectors are numbered clockwise, commencing with the first which is to the southward of east from the station. The common center of the circles and the radial lines is placed, in each case, at the point on the map corresponding to the station. Hayford showed that the calculation could be further has tened by using the principle of interpolation. The larger the 76 Testing Isostasy with the Plumb Line ring the more nearly alike are the deflections by its topog raphy on two stations close together. Hence a single com putation for a large ring suffices for each of a group of adja cent stations, significant errors not being introduced.* By compartmenting the topography, employing tem plates, and using interpolation, Hayford was able, without inordinate expense, to produce satisfactory values for the topographic deflections of the vertical at all of the hundreds of stations. Some of the results may be noted: (1) Because a plumb bob at a United States station is pulled gravitationally more by dry-land Canada than by the topography south of the United States, where there is so much deep sea, the meridian components of the topographic deflection at each United States station is negative. The minimum deflection of — CU.SS was found at a station on the south shore of Lake Superior; the maximum, — 64".97, at Santa Barbara, California. (2) Naturally, too, the maxima of the prime-vertical component appeared at stations near the eastern and western shores of the country. The maximum negative component, — 54".30, is at North End Knott Island, Virginia, only 130 kilometers from the trace of the 1,000-fathom contour of the Atlantic bottom. The maximum positive component re corded, + 104//.63, appeared at Point Arena, California, only 35 kilometers from the 1,000-fathom contour of the Pacific bottom. (3) The horizontal attraction of the high Cordilleran region had its expected systematic effect, so that at Mount Ouray, Colorado, and at all stations east of it the prime- vertical component is negative; and at all stations west of Mount Ouray this component is positive. (4) Specially rapid variation of the topographic relief was shown to cause correspondingly rapid changes in the * See Illustration No. 3 in Hayford’s 1909 Report. Testing Isostasy with the Plumb Line 77 deflection, whether in the meridian or in the prime vertical. A glance at Tables 4 and 5, or at the complete record in the Report, shows as a rule the relatively great difference between observed and topographic deflection at the individ ual station. How to explain such differences is the funda mental problem to which the greater part of the Report is devoted. Before attacking it, however, Hayford discussed an important subsidiary question: To what extent are the observed deflections related to the topography? In order ROCKY
Figure 13. Section showing the relations of gcoid and spheroid, with and without isostatic compensation. to answer it, he constructed, as far as was possible with the limited data, “the contour lines of the geoid graphically, starting with the observed deflections of the vertical as a basis.” (Report, p. 57.) The principle that in general the plumb line on the actually rugged earth can not coincide with the radius of a perfect spheroid is illustrated in Figure 13. The relation of vertical and radius is shown under two hypotheses: first, that the continent shown is not at all balanced isostatically by the oceanic sector; second, that there is such balance, the depth of compensation being relatively small. In both cases, each vertical at the surface deviates from the radius that passes through the same superficial point, but the deviation is much greater where there is no isostasy. Since the geoid is 78 T esting Isostasy with the P lumb Line everywhere at right angles to the vertical, the geoid is arched above the spheroid in the continental region and depressed under the spheroid in the oceanic region. C onstruction oe t h e G e o id . Hayford further wrote as follows: By contour lines of the geoid are meant lines of equal eleva tion on the geoid surface, referred to the Clarke spheroid of 1866 as a reference surface, the spheroid being supposed to be in the position fixed by the adopted United States Standard (Geodetic) Datum. The contour lines serve to indicate clearly to the eye, and in a comprehensive manner, the departure of the geoid from the spheroid. The geoid surface is a surface which is everywhere normal to the direction of gravity (an equipotential surface), and it is that particular one of many such surfaces, lying at different elevations, which coincides with the mean sea surface over the oceans. Obviously, the mean sea surface must, with considerable accu racy, be everywhere normal to the direction of gravity. The mean sea surface is an existing physical representation of the geoid surface for the three-fourths of the earth covered by the oceans. No similar physical representation exists for the areas covered by continents. One may conceive of such a phys ical representation by supposing that narrow canals, say one foot wide, were cut down to a depth somewhat below mean sea level along the township boundaries of the land system over the United States. Such canals would form a rectangular system following approximately along meridians and parallels and approximately six miles apart in each direction. If the sea water were allowed free access to all these canals and were protected from all dis turbances, the surface of the water in the canals would every where become normal to the direction of gravity and would be at sea level and, therefore, would be a part of the surface of the geoid. One may think of the surface of the water in these hy pothetical canals as forming a concrete representation of that portion of the geoid which lies under the United States. The restriction in the preceding statement that the supposed canals must be very narrow (1 foot wide) is introduced because if the canals were supposed to be of considerable width the sup posed removal of masses to make the canals would change the Testing Isostasy with the Plumb Line 79 direction of gravity at various points and so produce a new geoid. The problem at present under consideration is that of con structing the contour lines which will represent the relation of the irregular geoid to the regular ellipsoid of revolution known as the Clarke spheroid of 1866, which is supposed to be in the position fixed by the adopted United States Standard Datum. The deflections of the vertical, as observed and shown in the tables . . . are slopes of the geoid, at the points of observation, with reference to the spheroid. Having given these slopes in the direction of the meridian and the prime vertical at these few points, the problem in hand is to construct the contour lines of the geoid. (Report, p. 58.) A concrete illustration of the method used in computing the deviation of the geoid from the spheroid is given by Bowie, in the following words :* If the deflection is 20 seconds of arc at a station where the geoid and spheroid surfaces intersect, and should this tilting continue without change for 40 miles, the two surfaces at the latter place would be 20 feet apart. The two sides of an angle of one second deviate 1 foot at 40 miles. . . . Along an arc of triangulation there are usually many stations at which the deflection of the vertical has been determined. Therefore, the variations of the geoid surface can be computed. A simple method is to assume that the tilting of the geoid at a station continues one-half the way to the next deflection station. Integration of all the tilting-slopes at many stations gives ap proximately the curvature of the geoid with respect to the ellips oid. The success of this part of Hayford’s investigation was only partial, for two reasons. In the first place, the number of stations occupied was quite insufficient to permit the con touring over the whole country. Secondly, the only prac tical method devised for drawing the contours could not give an absolutely reliable map of even those parts of the vast area where stations were comparatively numerous. * W. Bowie, Prof. Paper 99, U. S. Coast and Geodetic Survey, 1924, p. 6. 80 Testing Isostasy with the Plumb Line Figures 14 and 15 are copies of parts of the United States map where Hayford dared to draft contour lines in some abundance. After discussion of the difficulties of drawing the contours and of interpreting the results, Hayford concluded as fol lows: A study in detail of the gcoid contours as shown on illustration No. 17 shows conclusively that, though the irregularities in the
Figure 14. The geoid in the northeastern United States. Contours in meters. The thin line is the 1,000-foot contour for topography. geoid are much too small to correspond to the computed topo graphic deflections, yet the geoid is not independent of the topog raphy. The general features of the topography which cover large areas are indicated by the geoid contours. On the geoid the greatest elevations correspond approximately in position to the greatest mountain masses. Depressions and valleys in the geoid correspond to the greater depressions and valleys in the land surfaces. The steepest slopes of the geoid tend to corre Testing Isostasy with the Plumb Line 81 spond in position to the steepest general slopes of the land sur face. A contour of the geoid tends to follow each coast line. The smaller features of the topography are not shown in the geoid contours. It is possible that, if a larger number of ob served deflections were available and were used in constructing the geoid contours, smaller features of the topography might show an effect on the geoid contours. The contradictions between the geoid and the topography are few in comparison with the agreements. That is, the directions
Figure IS. The geoid in an east-west belt from Kansas to Colorado. Contours of the geoid in meters. Three contours for topography in multiples of 1,000 feet. of slopes on the geoid agree generally with the general slopes of the topography. (Report, p. 65.) R e c o g n it io n o f I so st a sy . From the relation between geoid and topography and from the excess of the topo graphic deflection of the vertical over the observed deflec tion, Hayford concluded “that some influence must be in operation which produces an incomplete counterbalancing of the deflections produced by the topography, leaving much smaller deflections in the same direction.” Thus his un rivaled data led him to a view that had been held in principle 82 Testing Isostasy with the Plumb Line by Bouguer and Boscovich of the eighteenth century and by Petit, Pratt, Airy, Clarke, Helmert, and other geodesists of the nineteenth century. All these other investigators had based their conclusion on observations made in Europe, Asia, and South America. With greater wealth of facts assembled in North America, Hayford was driven to the same idea: ex tensive highlands must be underlain by rock with density smaller than that of the average rock constituting the skin of the earth; and this average density is smaller than that of the rock underlying the ooze of the sea bottom. A close approach to complete isostatic balance was indicated for United States territory. We note again Hayford’s principal object: to find the di mensions of the ellipsoid that would best fit the geodetic observations. Before reaching that goal, he soon saw that answers to two other questions should be sought: (1) How close is the approach to ideal isostasy? (2) To what depth or depths do the implied abnormalities of density in the superficial earth-shell extend? To the discussion of these problems one hundred pages of the Report are devoted. Hayford’s thoroughness was in part prompted by his convic tion that the subject is significant in geophysics, quite apart from the field of practical geodesy. Here again, in the fol lowing abstract, the reasoning and procedure will be de scribed in actual quotations, even though some of the essen tial ideas and definitions have already been presented. Before entering on details, we glance at Figure 16, which illustrates the principle embodied in Figure 13. Figure 16 is a vertical section of the lithosphere, in this case represented without curvature and containing a mass with abnormally high density (shaded). If this mass were replaced by rock of normal density, and if there were no other horizontal variation of density all around the globe, the surface of the geoid would be parallel to the level, rocky surface, as indi cated by the broken line. If there is no compensation for Testing Isostasy with the Plumb Line 83 the mass of excess density, the equipotential surface or geoid would be arched above that mass (uppermost continuous curve). If the mass of excess density is compensated, the geoid must be arched, but much less strongly (lower continu ous line). Since the vertical is always at right angles to the geoid, the deflection of the vertical would reflect these three different conditions. Hayford wrote: If the earth were composed of homogeneous material, its figure of equilibrium, under the influence of gravity [sic—meaning
G EO ID W IT H NO ISOSTASY GEOID WITH SPHEROID J. ISOSTASY
Depth of Compensation (isostasy assumed)
Figure 16. Geoid and spheroid, with and without isostatic compensation for a subterranean mass of abnormal density. (Curvature of spheroid not shown.) gravitation] and its own rotation, would be an ellipsoid of revolu tion. The earth is composed of heterogeneous material which varies considerably in density. If this heterogeneous material were so arranged that its density at any point depended simply upon the depth of that point below the surface, or, more accurately, if all the material lying at each equipotential surface (rotation con sidered) was of one density, a state of equilibrium would exist and there would be no tendency toward a rearrangement of masses. If the heterogeneous material composing the earth were not arranged in this manner at the outset, the stresses produced by gravity would tend to bring about such an arrangement; but as the material is not a perfect fluid, as it possesses considerable 84 Testing Isostasy with the Plumb Line viscosity, at least near the surface, the rearrangement will be imperfect. In the partial rearrangement some stresses will still remain, different portions of the same horizontal stratum may have somewhat different densities, and the actual surface of the earth will be a slight departure from the ellipsoid of revolution in the sense that above each region of deficient density there will be a bulge or bump on the ellipsoid, and above each region of excessive density there will be a hollow, relatively speaking. The bumps on this supposed earth will be the mountains, the plateaus, the continents; and the hollows will be the oceans. The excess of material represented by that portion of the continent which is above sea level will be compensated for by a defect of density in the underlying material. The continents will be floated, so to speak, because they are composed of relatively light material; and, similarly, the floor of the ocean will, on this supposed earth, be depressed because it is composed of unusually dense material. This particular condition of approximate equilibrium has been given the name isostasy. The adjustment of the material toward this condition, which is produced in nature by the stresses due to gravity, may be called isostatic adjustment. The compensation of the excess of matter at the surface (con tinents) by the defect of density below, and of surface defect of matter (oceans) by excess of density below, may be called the isostatic compensation. Let the depth within which the isostatic adjustment is com plete be called the depth of compensation. At and below this depth the condition as to stress of any element of mass is isostatic; that is, any element of mass is subject to equal pressures from all directions as if it were a portion of a perfect fluid. Above this depth, on the other hand, each element of mass is subject in gen eral to different pressures in different directions—to stresses which tend to distort it and to move it. In terms of masses, densities, and volumes, the conditions above the depth of compensation may be expressed as follows: The mass in any prismatic column which has for its base a unit area of the horizontal surface which lies at the depth of compen sation, for its edges vertical lines (lines of gravity) and for its upper limit the actual irregular surface of the earth (or the sea surface if the area in question is beneath the ocean), is the same as the mass in any other similar prismatic column having any Testing Isostasy with the Plumb Line 85 other unit area of the same surface for its base. To make the illustration concrete, if the depth of compensation is 114 kilo meters below sea level, any column extending down to this depth below sea level and having 1 square kilometer for its base has the same mass as any other such column. [See Figure 5, p. 49 in this book.] One such column, located under a mountainous region, may be 3 kilometers longer than another under the seacoast. On the other hand, the solid portion of such a column under one of the deep parts of the ocean may be 5 kilometers shorter than the column at the coast. Yet, if isostatic compensation is complete at the depth 114 kilometers, all three of these columns have the same mass. The water above the suboceanic column is under stood to be included in this mass. The masses being equal and the lengths of the columns different, it follows that the mean density of the column beneath the mountainous region is three parts in 114 less than the mean density of the column under the seacoast. So, also, the mean density of the solid portion of the suboceanic column must be greater than the mean density of the seacoast column, the excess being somewhat less than five parts in 114 on account of the sea water being virtually a part of the column. Hayford’s introduction of the expression “depth of com pensation” recalls Boscovich’s verb “compense.” Hayford wrote: The idea implied in this definition of the phrase “depth of com pensation,” that the isostatic compensation is complete within some depth much less than the radius of the earth, is not ordi narily expressed in the literature of the subject, but it is an idea which it is difficult to avoid if the subject is studied carefully from any point of view. It is proposed, therefore, in this investiga tion to assume that the depth of compensation is much less than the radius and to treat it as an unknown to be determined. (Report, pp. 67-8.) We have noted that economy of labor and therefore in financial cost can be secured by making certain simplifying assumptions before proceeding to compute topographic de flections. So it is here, in the case where the effect of isostatic compensation on the plumb line is to be evaluated. 86 Testing Isostasy with the Plumb Line One of the second set of assumptions was at once seen to be justified: the force of gravity was supposed constant in all parts of the layer of compensation. That force at sea level increases about one half of one per cent between equator and pole, and not far from the same amount in passing downward to a level of 100 kilometers from the earth’s surface. How ever, both rates of change are so small that they have negli gible influence on deflections of the plumb line. Hence Hayford thought it fair to attribute the constancy of pres sure at the depth of compensation essentially to the amount of matter, mass, above that depth, rather than to insist on constancy of weight for a unit volume of that matter. Two simplifying and arbitrary assumptions were made in the belief that, while they would greatly facilitate computa tion, they would entail no serious errors in the results, whether geodetic or geophysical; and yet here it was not im mediately obvious that serious error might not be caused. First, it was supposed, for the purpose of computation, that there is perfect isostatic compensation of every feature of the earth’s relief, even to that with an infinitesimal ground- plan. Secondly, it was assumed that the compensation is uniformly distributed along each of the earth’s radii, down to the depth of compensation. Hayford did not believe either assumption to be in accord with fact. He knew that small features like the average volcanic cone, a narrow can yon, or a Yosemite cliff, are stable because of the strength of the surface rock. In other words, absolutely local com pensation is out of the question. Doubtless Hayford was just as clearly aware that compensation can not be abso lutely uniform along any radius of the earth. His plan was to calculate isostatic deflections in a way that was actually possible with finite resources in labor; then, from results which could not be quite accurate, to estimate the horizontal dimensions of the largest area in the United States that is Testing Isostasy with the Plumb Line 87 out of isostatic equilibrium, and also to estimate the excess or deficiency of mass beneath that area. For economy of labor, Hayford adopted an additional convention: he supposed the isostatic compensation to ex tend everywhere to a fixed depth, measured downward from the solid surface of the earth. That is, the top of the layer of compensation was taken to be at the rocky sur face in each land area and at the sea bottom in oceanic areas. By means of actual tests he demonstrated that the corresponding results of computation are essentially like those derived if the depth of compensation be everywhere measured from sea level or geoid. E ff e c t o f I so sta tic C om pe n sa t io n o n t h e D ir e c t io n of t h e V e r t ic a l . That the effect of an attracting topo graphic element on the plumb F igure 17. Section illustrating the line must be more or less per Hayford compensation for a mass fectly offset by the effect of the close to a station. corresponding compensation for the element is graphically illustrated in Figures 17 and 18. In each drawing S represents the station; c the center of gravity of the topographic element (shown in black); C, the center of its compensation (shaded). Figure 18, a section of the whole earth, shows the relations where two elements, each far around the curve of the earth, are considered. 88 T esting Isostasy with the Plumb Line Here the length of each element and the length of its com pensatory column are much exaggerated beyond the scale set by the radius of the globe. Under the assumptions adopted by Hayford, there is a comparatively simple relation between the topographic de flection of the vertical, due to any ring around a station, and the reversed-sign deflection produced by the compensation
F igure 18. Section illustrating the Hayford compensation for a mass distant from a station. under that ring. For each ring and each trial-depth of com pensation there was calculated a factor by which the topo graphic deflection, already found for the station, should be multiplied to give the corresponding isostatic compensation. On p. 69 of the Report is a formula, (2), which gives the component (Dc) of the deflection at a station above sea level, “produced by the compensating defect of mass com prised within a stratum hi statute miles thick, lying within a compartment limited as before.” The other symbols in Testing Isostasy with the Plumb Line 89 the formula have the same meanings as in equation (1), p. 71 of this book. r' + V(r')2 + h\ D c = h i 2 —12".44 ^ (sin a' sin a i ) loge ri + Vr J + h\ ( ) Since, by hypothesis, bh = bihlt r'+V(r')» + ftj (2a) D c = — 12".44 - 7 h (sin a ' — sin a i ) loge — ,------A 6 n+Vrf+A*r i + Vrl + hi There follows another formula giving the factor (F), by which D, the topographic deflection, must be multiplied to secure the resultant deflection D +DC due to both the topog raphy and the compensating defect or excess of mass below the surface. . . . The factors F have been computed from this formula for the rings used in computing the topographic deflec tions and for various assumed depths of compensation (hi). . . . The factor, F, is evidently the same for a whole ring. . . . The mass above sea level in any compartment and the compen sating defect of mass are equal. The latter has an effect in pro ducing a deflection at the station which is slightly smaller than the former, simply because much of the compensating defect of mass lies far below the horizon of the station. The angles of de pression below the horizon of the station to the different parts of the compensating defect of mass being the same for all compart ments in the same ring, evidently F, depending implicitly as it does upon the depression angles, should be the same. (Report, p. 71.) The computed values of F are given in Table 7 (p. 90). Hayford gave a few examples to illustrate the meaning of the factors. Let the depth of compensation be held at one of the suggested values, namely at 113.7 kilometers, and first let the effect of the compensation for a mountain at the great distance of 3,400 kilometers (in Ring 1) on the vertical be considered. The positive mass, A, of the mountain is compensated by uniform deficiency of mass, totaling the quantity C, through a vertical column 113.7 kilometers long and immediately beneath the mountain. The factor F for 90 T esting Isostasy with the Plumb Line this depth of compensation and for Ring 1 is 0.001, so that the negative deflection produced by C is 0.999 of the positive deflection produced by A ; in other words, the net result is to give at the station concerned a deflection only 0.001 of T able 7 REDUCTION FACTORS, F.
Values of F corresponding to depths of compensation Ring Outer radius of ring (km) 162.2 km 120.9 km 113.7 km 79.76 km 55.92 km 29 0.1915 ______.997 28 0.2729 — — — .997 .996 27 0.3893 — .997 .997 .996 .995 26 0.5551 .997 .996 .996 .995 .992 25 0.7915 .996 .995 .995 .992 .988 24 1.129 .995 .993 .992 .988 .983 23 1.609 .992 .989 .988 .983 .976 22 2.295 .988 .984 .983 .976 .965 21 3.272 .983 .979 .976 .965 .951 20 4.665 .976 .967 .965 .951 .930 19 6.653 .965 .954 .951 .930 .900 18 9.487 .951 .935 .930 .900 .859 17 13.53 .930 .906 .900 .859 .801 16 19.29 .900 .867 .859 .801 .721 15 27.50 .859 .813 .801 .721 .618 14 39.22 .801 .736 .721 .618 .493 13 55.92 .721 .638 .618 .493 .358 12 79.76 .618 .517 .493 .358 .234 11 113.73 .493 .382 .358 .234 .139 10 162.27 .358 .253 .234 .139 .077 9 231.3 .234 .153 .139 .077 .040 8 329.8 .139 .086 .077 .040 .020 7 470.3 .077 .045 .040 .020 .010 6 670.8 .040 .022 .020 .010 .005 5 957.9 .020 .011 .010 .005 .003 4 1369 .010 .006 .005 .003 .001 3 1962 .005 .003 .003 .001 .001 2 2828 .003 .001 .001 .001 .000 1 4126 .001 .001 .001 .000 .000 that produced by A alone. If the mountain is in Ring 9, other conditions remaining the same, the net deflection is 0.139 of that produced by A alone. If the station is at the foot of the mountain and 7 kilometers from its summit, most parts of the compensation C will have high angles of depres Testing Isostasy with the Plumb Line 91 sion from the station, where, therefore, they will have little effect on the direction of the vertical at the station, though they must there decrease the intensity of gravity below the value it would have if A were not compensated. On the other hand, the attraction of the mountain mass A will have nearly full effect on the direction of the vertical at the sta tion. The summit of the mountain is in Ring 18; hence from the table it is seen that the compensation of this part of the mountain diminishes that full effect by only seven per cent. For portions of the mountain still nearer to the sta tion the ratio of the negative effect of C to the positive effect of A is still smaller, and the reduction is correspondingly larger than 0.930. It may be noticed that in the table of reduction factors F, with the exception of the column headed 120.9, the figures are the same in the various columns. The columns differ from each other simply in having the figures displaced vertically. This arises from the fact that the successive assumed depths of com pensation, with the one exception stated, are the same as the outer radii of the successive rings. An inspection of the formula shows that the relation stated is true when such a selection has been made. The arbitrary selection of these particular depths, therefore, saved considerable time in computing the factors F, and was allowable in the beginning of the investigation when little was known as to the most probable depth of compensation. The selection of the depth, 120.9, to which this time-saving de vice does not apply, was made later in the investigation, after the most probable depth was approximately known. (Report, P- 72.) The sum of the resultant deflections due to isostatic com pensation for all the rings around a given station can be compared with the sum of the matching topographic deflec tions; and the difference between the two sums can be com pared with the observed deflections. Tables 4 and 5 illus trate such comparisons. Hayford’s complete tables of the kind are too elaborate to be copied in this book. 92 Testing Isostasy with the Plumb Line The summary of results may be quoted in Hayford’s own words: The computed deflections, with isostatic compensation consid ered, are, as a rule, much smaller than, and of the same sign as, the topographic deflections. There are some exceptions . . . but they are not numerous. The computed deflections, with isostatic compensation con sidered, ordinarily decrease numerically as the assumed depth of compensation decreases. There are rare exceptions. . . . The computed deflection, with isostatic compensation consid ered, ordinarily agrees much more closely with the observed de flection than does the topographic deflection. (Report, p. 73.) The unexplained part of each station deflection is called a deflection residual. Having tabulated all the residuals, Hay- ford was ready to enter on his main problem, namely, to find the dimensions of the ellipsoid that would fit the observations in the United States better than the Clarke ellipsoid of 1866 fits them. The method adopted for this operation was that of trial and error. Five different hypotheses regarding isostasy were made. The first assumed no isostasy what ever, or thorough rigidity of the earth. The second assumed compensation at zero depth. The other hypotheses assumed the depth of compensation to be at the respective depths of 162.2, 120.9, and 113.7 kilometers. The depths of 162.2 and 113.7 kilometers equal the lengths of the outer radii of Rings 11 and 12, this equality, as we have seen, facilitating compu tation in the two cases. The depth of 120.9 kilometers was chosen after preliminary exploration of the problem, as a value close to the one finally indicated. The residuals were calculated for each of the five hy potheses. According to mathematical theory, that hy pothesis is the most probable which makes the sum of the squares of the residuals a minimum. The five sums are stated in Table 8, where the corresponding solutions of Hay- ford’s problem are distinguished by capital letters. Testing Isostasy with the Plumb Line 93 From the residuals of solutions E, H, and G, the conclusion was reached that the most probable depth of compensation is 112.9 kilometers, which agrees so closely with the depth used in solution G, 113.7 kilometers, that it is not certain that solution G can be improved upon. (Report, p. 115.) This conclusion was thought to be corroborated by other evidence, derived from detailed discussion of the residuals. After announcing the general result, Hayford proceeded to examine various sources of error, each of which contributes something to the residuals of the adopted solution G. . . . Among these
T able 8 DATA FOR TESTING VARIOUS ISOSTATIC HYPOTHESES Sum of squares Solution B (extreme rigidity)...... 65,434 Solution E (depth of compensation 162.2 km)...... 8,220 Solution H (depth of compensation 120.9 km)...... 8,020 Solution G (depth of compensation 113.7 km)...... 8,013 Solution A (depth of compensation zero)...... 13,922 sources have been the astronomic observations of latitude, longi tude, and azimuth, the observation of angles, the measurements of base lines in the triangulation, the errors in the computations of topographic deflections due to the errors and incompleteness of available maps and also to the method of computation, the errors in the assumed densities, and, finally, errors in the com puted coefficients used in the equations. The detailed examina tion of these separate sources of error has shown that no one class of errors nor the combination of all classes enumerated is sufficient to account for such large residuals as those in solution G. These residuals must be due mainly to some other cause. . . . From a long and careful study of the details of the evidence the writer [Hayford] is firmly convinced on two main points. The first is that the residuals of solution G are smaller than those of any other solution made, simply because the assumption upon which solution G is based is a closer approximation to the truth, as a statement of a general law controlling the variation of subsurface densities, than any of the other assumptions made. The assumption for solution G is that the isostatic compensation 94 Testing Isostasy with the Plumb Line is complete and uniformly distributed throughout the depth 113.7 kilometers. The second main point is that the residuals of solution G are mainly due to irregular variation of subsurface densities from the law indicated in the preceding paragraph, the densities being excessive for various areas of greater or less extent and deficient for various other areas. No general law controlling these varia tions has, as yet, been discovered by the writer. (Report, pp. 132, 133.) Statistical T ests of C o nc lu sio ns. Are the conclusions that the E, H, and G solutions are much nearer the truth than the B and A solutions, and that solution G is nearest the truth, dependent on the effects of a few large residuals? Are these conclusions dependent upon and vitiated by the geographic grouping of residuals of like sign to which attention has been di rected? Do astronomic observations in all parts of the area treated and all three classes of astronomic observations cooperate in confirming the conclusions reached? As aids in answering these questions Hayford compiled two sets of tables, respectively stating for groups of stations: (1) the mean value of the squares of the residuals in the various groups; (2) mean values of the residuals without regard to sign; (3) percentage of residuals smaller than 2,/.00; (4) percentage of the residuals greater than 5//.00; and (5) the maximum residual in each group. One of the assemblages of mean values of the residuals, and therewith the most reliable test, is here copied (Table 9). Additional data for testing the solution appear in Table 9a, which gives the values of the residuals of the same groups, without regard to sign. The other three sets of data corrob orate the conclusion drawn from the first and second. The statistical examination led to the following con clusions : (1) That solution B (extreme rigidity) is much farther from the truth than any of the other solutions and that this conclusion is not dependent upon nor vitiated by a few large residuals or by the geographic grouping of the residuals and is a necessary con- Testing Isostasy with the Plumb Line 95
T able 9 MEAN VALUES OF THE SQUARES OF THE RESIDUALS IN VARIOUS GROUPS OF U. S. STATIONS
Solution B Solution E Solution H Solution G Solution A (extreme (depth of (depth of (depth of (depth of rigidity) compen. compen. compen. compen. 162.2 km) 120.9 km) 113.7 km) zero) All U. S. observations, 507 residuals 129.06 16.21 15.82 15.81 27.46 Northeastern group, 118 residuals 112.46 10.03 10.14 10.17 15.37 Latitude observ’ns, 58 res. 81.16 7.71 7.77 7.78 10.99 Longitude observ’ns, 22 res. 93.14 7.26 8.52 8.82' 20.97 Azimuth observ’ns, 38 res. 171.41 15.19 14.70 14.61 18.80 Southeastern group, 105 residuals 41.57 13.02 13.09 13.11 15.09 Latitude observ’ns, 53 res. 29.35 8.84 9.36 9.47 13.11 Longitude observ’ns, 16 res. 29.30 6.39 5.91 5.83 5.28 Azimuth observ’ns, 36 res. 65.03 22.12 21.78 21.69 22.37 Central group, 102 residuals 86.22 16.01 16.17 16.23 20.07 Latitude observ’ns, 63 res. 43.64 16.84 16.81 16.84 19.45 Longitude observ’ns, 15 res. 179.07 11.66 13.05 13.39 23.64 Azimuth observ’ns, 24 res. 139.94 16.55 16.42 16.38 19.48 Western group, 182 residuals 214.31 22.18 20.88 20.78 46.57 Latitude observ’ns, 91 res. 132.09 17.14 15.56 15.32 27.10 Longitude observ’ns, 26 res. 203.70 8.93 8.41 8.59 73.26 Azimuth observ’ns, 65 res. 333.66 34.53 33.31 33.30 63.16
T able 9a MEAN VALUE OF RESIDUALS WITHOUT REGARD TO SIGN
Solution B Solution E Solution 11 Solution G Solution A All U. S. observations, 507 residuals 8".86 3".06 3".04 3".04 3".92 Northeastern group, 118 res. 8 .97 2 .57 2 .60 2 .60 3 .09 Southeastern group, 105 res. 5 .07 2 .88 2 .89 2 .89 3 .10 Central group, 102 res. 6 .44 3 .02 3 .06 3 .07 3 .54 Western group, 182 res. 12 .34 3 .50 3 .40 3 .40 5 .14 96 Testing Isostasy with the Plumb Line elusion regardless of what class of observations is utilized (lati tudes, longitudes, or azimuths). The evidence is practically unanimous on this point. (2) That solution A (depth of compensation zero) is farther from the truth than any of the three solutions G, H, and E (depth of compensation 113.7, 120.9, and 162.2 kilometers, respectively), but much nearer the truth than solution B (extreme rigidity), and that this conclusion is nearly free from doubt due to the in fluence of exceptionally large residuals, to geographic grouping of residuals, or to contradiction between different classes of astronomic observations. (3) That the preponderance of evidence is in favor of solution G . . . being nearer the truth than either solutions H or E . . . but that this conclusion is drawn from conflicting evidence, indi cating that the nearness of approach to the truth is so nearly the same in these three solutions that the choice between them is made uncertain by the influence of a few unusually large residu als, and by the influence of the geographic grouping of residuals. Moreover, the three classes of astronomic observations do not agree in the choice among these three. In other words, though it is certain that an approach to perfect isostatic compensation exists extending to a moderate depth (certainly not greater than 200 kilometers) if it is uniformly distributed, the precise depth is difficult to determine from the data in hand. (Report, p. 139.) Hayford attempted to determine whether the depth of compensation is constant. He found that while there are indications that the depth of compensation is greater in the eastern and central portions of the United States than in the western portion, the evidence is not strong enough to prove that there is a real difference in depth of compensation in the different regions. Possibly such a difference may exist, but it is not safe now to assert that it exists. On pp. 143-6 of his book he describes the method of com puting the most probable depth of compensation. His gen eral conclusion reads as follows: For the United States and adjacent areas, if the isostatic com pensation is uniformly distributed with respect to depth, the most probable value of the limiting depth is 70 miles (113 kilo Testing Isostasy with the Plumb Line 97 meters), and it is practically certain that the limiting depth is not less than 50 miles (80 kilometers) nor more than 100 miles (160 kilometers). Hayford then gives the reasons why he supposed isostatic compensation to be “uniformly distributed with respect to depth from the surface to the limiting depth of compensa tion.” . . . This assumption was adopted as a working hypothesis, because it happens to be that one of the reasonable assumptions which lends itself most readily to computation, and because it seemed to be the most probable simple assumption. With regard to the second of these reasons he first consid ered the locus of isostatic adjustment in an earth supposed to be hot enough to have a thin, strong crust resting on a liquid substratum (recalling Airy’s conception of isostasy). In this case correcting flow would be in the substratum and therefore relatively close to the surface. According to Dar win’s assumption that the planet is a competent, elastic structure, solid throughout, any isostatic adjustment should take place by flow at various depths but all comparatively great. According to Chamberlin’s planetesimal hypothesis, the isostatic compensation would be greatest at a level slightly below the surface, and from that point would decline at a vary ing rate, which rate increases rapidly at first and at greater depths decreases slowly, approaching zero at great depths. . . . These different considerations as to the probable distribution of isostatic compensation with respect to depth are not mutually exclusive. It may be that the actual distribution is a resultant of several or all of the actions and modifying influences which have been indicated briefly. Some of these tend to produce a uniform distribution of isostatic compensation near the surface, some to produce it at moderate depths neither very near the sur face nor very near the limiting depth of compensation, and some tend to produce a maximum near the limiting depth. Therefore it has seemed that the most probable simple assumption is that 98 Testing Isostasy with the Plumb Line the compensation is uniformly distributed from the surface to the limiting depth. It is not supposed that at the limiting depth of compensation there exists a perfectly abrupt change of conditions with respect to compensation. But it is believed to be possible that the de crease of isostatic compensation from its mean value to zero may all take place within so small a range of depth that the difference between the actual mode of distribution and the abrupt change postulated in the stated assumption may not be capable of de tection by the geodetic observations. Hence, it is deemed justi fiable to make the assumption in the form stated, which is such as to lend itself most readily to computation. It should be noted that each of the considerations brought for ward in the preceding paragraphs indicates that the isostatic compensation must be sensibly limited to some finite depth much less than the radius of the earth. The writer [Hayford] knows of no plausible conception of the conditions within the earth that would lead one to believe that isostatic compensation extends to the center. Hence, throughout this investigation it is assumed that, whatever the mode of distribution of the isostatic compen sation with respect to depth, it extends to a limiting depth which is but a small fraction of the radius. While it seems desirable, in connection with the present inves tigation, that the first assumption made as to the distribution of compensation should be a reasonable one and, preferably, that it should be the most probable simple assumption, it was evident, at the outset, that a failure to make the best selection would not be fatal to ultimate success and would probably not even hamper the investigation. It appeared on the preliminary reconnais sance of the problem that the most efficient method of attack is probably to make some one assumption as to the distribution of the isostatic compensation with respect to depth, to make full computations on this assumption, and then to test other assump tions by comparison with this one; not by complete new compu tations, but by a computation of the small differences in com puted deflections produced by the change from one assumption to the other. As various assumptions were to be tested, it was not of paramount importance which should be tested first. Rela tive ease of computation was properly one of the controlling elements in making the choice. Testing Isostasy with the Plumb Line 99 By the method described, Hayford proceeded to test the hypothesis that the compensation is complete and uniformly distributed through a 10-mile (16-kilometer) stratum at some depth well below the surface. He found that, if the bottom of this stratum were at a depth of 37 miles (59.5 kilometers), the deflection residuals would be about as well explained as on the assumption ruling the main investiga tion. Further, it was found that, if the compensation be sup posed uniformly distributed in any stratum whose thickness has a value between 10 miles and 71 miles, the center of grav ity of any vertical element of the stratum is situated at a depth of 32 miles or slightly less to 35.5 miles below the sur face. These results have an important bearing on Airy’s theory of isostasy. Another hypothesis, that the compensation decreases at a uniform rate from the surface to zero at a limited depth, gave the limiting depth at 109 miles or 175 kilometers. Then comparison was made with a hypothesis of decrease of compensation, at a diminishing rate, all the way to the earth’s center—a mode of compensation suggested by T. C. Chamberlin. In this case the center of gravity of the compensation was found to be not far from 71 miles or 113.7 kilometers below the surface. Finally, Hayford considered briefly Fisher’s modification of the Airy compensation, under the caption “floating crust hypothesis.” The conclusion was that the evidence is “sufficient to show that this hypothesis is not true for the United States.” (Report, p. 164.) D e g r e e oe I so sta tic C ompensation . H ow complete is the isostatic compensation in the United States? In its essential meaning Hayford’s answer was a notable contribu tion to geophysics and geology. The residuals of solution G furnish a test of the departures of the facts from the assumed condition of complete isostatic compen 100 Testing Isostasy with the Plumb Line sation uniformly distributed to a limiting depth of 113.7 kilo meters. In order to obtain definite ideas, let the whole of the residuals of this solution be credited to the incompleteness of the compensation. The conclusion as to the completeness of the compensation will then be in error in that the actual approach to completeness will be considerably closer than that represented by the conclusion—that is, the conclusion will be an extreme limit of incompleteness rather than a direct measure. For by this process of reasoning every portion of a residual of solution G, due to the departure of the actual distribution of compensa tion with respect to depth from the assumed distribution, or due to the error in the assumed mean depth of compensation, or to regional variation with a fixed depth of compensation, or due to errors of observation in the astronomic determinations and the triangulation which affect the observed deflection of the vertical, or due to errors of computation, is credited to incompleteness of compensation. (Report, p. 164.) “Such a limit to the degree of incompleteness of compen sation” is furnished by Table 10, which lists ten groups of stations, classified by geographical location. The various groups separately indicate the departure from complete compensation to be from less than 0.42 for group 5 to less than 0.05 for group 9, and all observations combined indicate the departure to be less than 0.094. Group 5 shows a much wider departure from the mean value 0.094 than does any other group. The remaining groups show a range from 0.05 to 0.13 only. The various values in the last column of the table do not indi cate the departures from complete compensation within the areas covered by the separate groups—that is, one must not rea son that complete isostatic compensation is approached within less than 0.05 by the arrangement of densities beneath the area covered by group 9, and that it is only approached within some what less than 0.42 beneath the area covered by group 5. It should be recalled, in this connection, that in computing the topographic deflections all areas within 4,126 kilometers of each station were considered and that the computed topographic deflection is not small for the outer rings of topography. These outer rings of topography which lie far beyond the limits of the particular group of observations which may be under considera Testing Isostasy with the Plumb Line 101 tion, necessarily produce deflections at the station unless isostatic compensation exists beneath said outer rings. Hence each value in the last column of the table is a test furnished by one group of the completeness of the isostatic compensation in and around the United States, rather than a test of the completeness within the area covered by that group alone. For the United States and adjacent areas it is safe to conclude from the evidence just summarized that the isostatic compensa tion is so nearly complete on an average that the deflections of
T able 10 LIMIT TO THE DEGREE OF INCOMPLETENESS OF COMPENSATION
1 2 3 4 5 Mean of Mean topographic residual of Value in Number deflections solution G col. 4 Groups of residuals of without re without re divided by stations gard to sign gard to sign value in (seconds of (seconds of col. 3 arc) arc) 1 (Me., N. H., Mass., R. I.) 52 35.48 2.50 .07 2 (Conn., N. Y., Penn., Ohio, Mich.) 54 20.86 2.53 .12 3 (N. J., Penn., Del., Md., Va.) 49 35.79 3.33 .09 4 (Va., N. C., Tenn., Ga., Ala., Miss., La.) 50 23.85 2.72 .11 5 (Mich., Minn., Wis.) 53 9.13 3.86 .42 6 (Va., W. Va., Ky., Ohio, Ind., 111., Mo., Wis.) 51 18.42 2.37 .13 7 (Mo., Kan., Colo., Utah) 46 16.80 2.26 .13 8 (Utah, Nev., Cal.) 43 31.84 3.48 .11 9 (Cal., northern part) 57 60.15 2.83 .05 10 (Cal., southern part) 52 66.35 4.57 .07 All combined 507 32.26 3.04 .094 the vertical are thereby reduced to less than one-tenth of the mean values which they would have if no isostatic compensation existed. One may properly characterize the isostatic compen sation as departing on an average less than one-tenth from com pleteness or perfection. This statement should not be interpreted as meaning that there is everywhere a slight deficiency of compensation. It is probable that under some areas there is overcompensation, as well as undercompensation in others. . . . The average elevation of the United States above sea level is 102 Testing Isostasy with the Plumb Line about 2,500 feet. Therefore an average departure of one-tenth part from complete compensation corresponds to excesses or deficiencies of mass represented by a stratum only 250 feet thick on an average. . . . The writer [Hayford] believes that the stress-differences in and about the United States have been so reduced by the isostatic compensation that they are less than one-twentieth as great as they would be if the continent were maintained in its elevated position and the ocean floor maintained in its depressed position by the rigidity of the earth. (Report, p. 166.) . . . The United States is not maintained in its position above sea level by the rigidity of the earth but is, in the main, buoyed up, floated, because it is composed of material of deficient dens ity. (Report, p. 176.) Hayford’s estimate of 250 feet for the thickness of a plate of normal rock which would represent excess or deficiency of mass may not be far wrong for the interior of the United States, but Barrell has pointed out that Hayford’s ratio of one-tenth should give for coastal belts nearly three times the stated excess or deficiency. The reason for this conclusion is the fact that at coasts the relief to be compensated is of the order of 4,000 meters (minus an amount matching the mass of the ocean water), not 800 meters (2,500 feet), which represents the average elevation of the United States above sea level.* Amended Ellipsoid of Reference. Hayford closes his memoir of 1909 with a statement concerning the dimensions of the ellipsoid which, with his data, best fits the United States part of the earth. The values are given in Table 1. He further notes that computation based on the recognition of isostasy necessarily leads to dimensions that are some what larger than those derived in previous investigations. HAYFORD’S SECOND INVESTIGATION Between 1906 and 1909, energetic field work added 258 new geodetic observations to the 507 of the first investiga * J. Barrell, Jour. Geology, vol. 22, 1914, p. 300. Testing Isostasy with the Plumb Line 103 tion. All were reduced, and in 1910 Hayford published a second official volume entitled “Supplementary Investiga tion in 1909 of the Figure of the Earth and Isostasy.” The assumptions and methods of computation were practically identical with those used in the earlier test of isostasy. It suffices to note here merely the results bearing on our subject. The deflection residuals were discussed in groups, but the fact that no startling change was made in the general results can be illustrated by Table 11, which gives values for the United States as a whole.
T able 11 MEAN VALUES OF THE SQUARES OF THE RESIDUALS
Solution B E // G A Depth of compensation (km).. “infinite” 162.2 120.9 113.7 0 507 observations, 1909 Report. 129.06 16.21 15.82 15.81 27.46 733 observations, 1910 Report. 146.50 14.05 13.73 13.75 25.77 Hayford wrote: Solution H, having the smallest sum of the squares of the residu als, is probably the closest approximation to the truth. . . . Solution H is apparently slightly nearer the truth than solution G, but there is little basis for a choice between these two. . . . For the United States and adjacent areas, if the isostatic com pensation is uniformly distributed with respect to depth, the most probable value of the limiting depth is 76 miles (122 kilo meters), and it is practically certain that the limiting depth is not less than 62 miles (100 kilometers) nor more than 87 miles (140 kilometers). The most probable value of the limiting depth of compensation as derived from this supplementary investiga tion is only 6 miles (9 kilometers) greater than that derived from the main investigation. The estimated range of uncertainty has been narrowed to one-half the former estimate. (1912 Re port, p. 77.) The increase of 8 per cent, from 113 to 122 kilometers, in the estimated depth of compensation carries with it a similar 104 T esting Isostasy with the Plumb Line increase for the most probable depth corresponding to other assumptions that were made, in the earlier Report, as to the distribution of compensation in depth. For example, if the isostatic compensation is uniformly distributed through a stratum 10 miles (16 kilometers) thick, the most probable depth for the bottom of the stratum is 40 miles (65 kilo meters). The supplementary investigation has . . . strengthened the conclusion that a decided increase of accuracy [in determining the figure of the earth] is obtained by the recognition of isostasy. (1912 Report, p. 78.) CONCLUSIONS REGARDING THE DIMENSIONS OF UNCOMPENSATED LOADS Hayford’s two reports made it certain that the United States territory as a whole is in almost perfect, if not prac tically perfect, isostatic balance with the adjacent oceanic sectors of the earth. On the other hand, the deflection re siduals, grouped according to sign, prove the existence of regional, uncompensated loads. The spans and intensities of these loads are the data needed for estimating the strength of the earth-shells under the North American continent. The two investigations did not suffice to locate and meas ure the maximum load borne by the United States sector, for the triangulation network covered no more than 15 per cent of the country, the observations being confined to rela tively narrow belts. These belts included: a transconti nental belt centered near the 39th parallel of latitude; a north-south belt between the 94th and 99th meridians; a belt along the Great Lakes; belts along the Atlantic and Pacific coasts; and a belt following the Appalachian axis. Illustrations 5 and 6 of the 1912 Report show each belt to have many alternations of plus and minus areas, whether the plotting referred to prime-vertical or meridian deflec tions. For example, the transcontinental belt has ten posi Testing Isostasy with the Plumb Line 105 tive, and as many negative, areas for the prime-vertical de flections, and a dozen alternating positive and negative areas for the meridian deflections. The east-west lengths of the largest areas are 800 kilometers (prime-vertical, Nevada- Utah) and 1,100 kilometers (meridian, California-Nevada- Utah). But in each case the lack of observations to north and south of the belt makes it impossible to state the range in the span of this Cordilleran segment of the geoid. And it is the minimum mean span which is vital in the problem of strength underground. Thus the geoidal tests of isostasy oriented general ideas, but they did not, directly and alone, indicate the dimensions of the uncompensated loads. The testimony regarding de partures from isostasy were to be supplemented and made more precise by study of the intensity of gravity within the limits of the United States—the subject of chapters 5 and 6. It will there be found that, qualitatively and to some extent quantitatively, the humps and hollows in the geoid correspond well with the positive and negative departures of gravity from the respective theoretical values. 4 MEASUREMENT OF GRAVITY; COMPARISON OF INTENSITIES
We turn now to the second method of determining the figure of the earth and a corresponding test for the theory of isostasy. GRAVITATION The mutual attraction of two masses, m and M, whose centers of attraction are separated by the distance a, is equal
4 4 4 4 4 4 4
Figure 19. Equal attractions of cylinders of different lengths but at differing distances below a given level. to k.m.M / a2, where k is the gravitational constant (6.67 X 10-8 dyne in the centimeter-gram-second system of units). According to the same system, the unit of acceleration of gravity is one gal (a modern coinage from the name Galileo), equal to 1,000 milligals. The unit of force that causes this unit of acceleration is the dyne, equal to 1,000 millidynes. 106 Gravity; Intensities 107 Figures 19, 20, and 21, copied from a memoir by Vening Meinesz and Wright, graphically illustrate how distance affects the gravitational attraction of a mass on a particle.* The assumed mass constitutes a cylinder with the density
4 8 16 24 32 40
Figdre 21. Attractions of identical cylinders at different depths below point- masses on a given level. of 1.0, radius of one centimeter, and variable height, as shown in the drawings. In Figure 19 each cylinder exerts an attraction of 4 X 10-8 dyne on unit mass situated at the dot below the digit 4. * F. A. Vening Meinesz and F. E. Wright, Publications of the U. S. Naval Ob servatory, vol. 13, App. 1, 1930, p. 50. 108 Gravity; Intensities In Figure 20 the numbers, when multiplied by 10~8, give respectively the attraction exerted by each cylinder on unit mass located at the upper end of its axis. The numbers en tered in Figure 21, when multiplied by 10—s, give the re spective attractions exerted by cylinders of equal volume and density on unit mass located at the dots just under the different numbers. The same memoir contains the data of Table 12, which states the attraction of a cylinder with unit density, radius of 1 kilometer, and height of 1 kilometer on unit mass located on the produced axis of the cylinder and H kilometers from its upper surface.
T able 12 ATTRACTION OF A CYLINDRICAL MASS 1 1 (Height of unit mass above Gravitational attraction top of cylinder; kilometers) (dyne or gal) 0.0 ...... 0.0246 .1 ...... 0217 .2 ...... 0192 .3 ...... 0169 .4 ...... 0150 .5 ...... 0132 .6 ...... 0117 .7 ...... 0104 .8 ...... 0093 .9 ...... 0083 1.0 ...... 0075 1.5 ...... 0046 2.0 ...... 0031 3.0 ...... 0016 4.0 ...... 0010 5.0 ...... 0007 10.0 ...... 0002 The three sets of diagrams and the table may also help one to understand the relations of any field of gravity to the theories of isostatic compensation. Because the deeper earth-shells are denser than those overlying, the force of gravity must in general increase with increase of depth until a maximum of the force is reached. Under certain assumptions Benfield estimates that maximum Gravity; Intensities 109 to be 2.5 per cent greater than gravity at the surface, and locates the maximum at about 2,500 kilometers below sea level. Below that depth the force diminishes with depth, to become zero at the earth’s center of mass.1 As already noted by Hayford, the change of value is not significant in the discussion of isostasy. Allowing for it is not likely to serve any useful purpose until future study shall have deter mined more accurately the proper values to be assigned to the other variables involved. RELATION OF GRAVITY TO LATITUDE On a rotating, spherical, homogeneous planet the gravita tional attraction of the body would have a constant value at all points on the surface. However, the intensity of the planetary gravity (g) would vary with the latitude, being affected at any point outside the axis of rotation by the cen trifugal force (/) exerted at that point. Since / varies di rectly with the radius of the parallel of latitude on which the given point lies, / equals the centrifugal force at the equator (/<,) multiplied by the cosine of the latitude at the point. (See Figure 22.) At that point the gravitational attraction is diminished by an amount equal to / multiplied by the cosine of the latitude; hence the diminution may be expressed as /c,cos2<£. Thus the force of gravity at the point is expressible in terms of f e and of gravity at the equator (ge):
g = g o + f e - f e COS2
S = ge (1 + b s i n 24> — csin2 20). (4) According to assumptions made as to the distribution of density in the planet, the computed values of c vary slightly. FromJHelmert’s value, namely 0.000007, it would follow
F igure 22. The influence of latitude on the intensity of gravity. that the spheroidal surface is depressed in maximum about 3 meters below the exact ellipsoid of revolution, the spheroid having the same axes as the ellipsoid. The maximum de pression occurs at latitude 45 degrees.2 If the earth’s figure were an exact ellipsoid, the difference of gravity at pole and equator, and therewith the flattening of the figure, could be found if the force were measurable with complete accuracy at only two points, located at differ ent latitudes. Since, however, small errors of observation Gravity; Intensities i l l are unavoidable, and also because there are local abnormali ties of gravity, measurements of gravity at a large number of stations are necessary. From stich abundant data acci dental errors tend to cancel out more or less perfectly.- Let it be assumed that the spheroid of reference is known with accuracy, and that the values of gravity at a number of stations have been reduced to the values at corresponding points on the geoid, vertically below the respective stations. If these reduced values differ systematically from those cal culated for the station latitudes and longitudes on the spheroid of reference, the differences indicate anomalies of mass below the region investigated or at depth in the vicinity of that region. This general truth suggests a means of deciding whether or not the earth’s topography is com pensated. MEASUREMENT OF GRAVITY Apparatus for measuring the acceleration of gravity at any accessible point may be briefly described. The most widely used method is based on the fact that the force of gravity controls the time of oscillation of a fric tionless pendulum with a given length, the amplitude of the swing being small. This time (t) varies inversely with the square root of the local acceleration of gravity (g), and di rectly with the square root of the length of the pendulum (l). The connecting equation may be written: g = ir2l/t2. At Greenwich, England, and at sea level, a pendulum making a complete oscillation in two seconds, under standard condi tions of air pressure and temperature, has a length of about 39.14 inches or 99.4 centimeters. The formula gives at once a rather close approximation to the force of gravity at Greenwich. Until the beginning of the nineteenth century all pendu lums designed for the measurement of gravity were of the simple type, with heavy bob and supporting string or rod. i 12 Gravity; Intensities In spite of every precaution the results were not satisfactory. In 1817 H. Kater conceived the reversible, rigid pendulum, an idea which is fundamental in the design of reliable modern apparatus. By 1887 such an instrument, with period of half a second and therefore of moderate bulk, had been de veloped by R. von Sterneck. Four years later T. C. Men denhall and E. G. Fischer of the United States Coast and Geodetic Survey made further improvement in the design, and soon thereafter G. R. Putnam, using the Mendenhall instrument, occupied 25 stations in the United States. The pendulum apparatus more recently perfected by Vening Meinesz for use at sea has already answered some principal questions bearing on the main problem of this book. The efficiency of his invention and that of Hecker’s less ac curate apparatus for measurements over the ocean will be noted in the ninth chapter. In contrast with the pendulum instruments are various static gravimeters, which use the elasticity of solids or the elasticity of inclosed volumes of gas. Among these types are: (1) the apparatus developed by von Thyssen and Schleusener; (2) that of Haalck; (3) the “elastic pendulum” invented by Holweck and Lejay; and (4) the “Quarzsch- weremesser” of Norgaard.3 A close determination of the differences of gravity at a number of stations is now possible and may be made with comparative rapidity, but to attain full usefulness all these relative values must be referred to the absolute value of gravity at some base station, a value won after a prolonged and extremely delicate operation. Until the year 1936 it had been generally assumed that the most accurate measure ment of absolute gravity was that made at Potsdam, Ger many, and for many years values of gravity at other stations all over the world have been referred to Potsdam.4 There, at the height of 87 meters above sea level and at latitude Gravity; Intensities 113 52° 22'.86 and east longitude 13° 4'.06, the acceleration of gravity was found to be 981.274 ± 0.003 gals.* Old and new values of absolute gravity (g) at base stations are given in the following table (possible, though small, ranges of error omitted):
g at Potsdam, found by Station g, directly relative measurements Difference determined based on the stations (milligals) (gals) named (gals)
Potsdam 981.274 ______Vienna 980.862 981.283 +9 Paris 980.970 981.300 +26 Rome 980.343 981.270 - 4 Madrid 979.977 981.270 - 4 Padua — 981.260 -1 4 Teddington 981.181 981.261 -13 Washington 980.080 981.254 -2 0
If absolute gravity (g) at a base station and the period of an invariable pendulum (p) at that point are known, the force at any other station can be determined by a simple process. The same pendulum is swung under the same con ditions at base station and new station for times long enough to give the average rate of oscillation at each point. With P representing the period of oscillation at the new station and G the value of gravity there, we have the equation r _ P2 ■ K In practice, similarity of conditions is established as closely as possible by applying corrections for differences of tem * According to their quite recently determined value of absolute gravity at Washington, P. R. Heyl and G. S. Cook of the U. S. Bureau of Standards have reason to suspect that the hitherto accepted value at Potsdam is too high by an amount perhaps as much as 20 milligals. This excess comes out at about 13 milligals when the value at Potsdam is referred to observed absolute gravity, which has been measured by Clark at the National Physical Laboratory, Tedding- ton, England. See J. S. Clark, Trans. Roy. Soc. London, vol. 238a, 1939, p. 96; also W. D. Lambert’s summary statement on p. 330 of “Internal Constitution of the Earth” (New York, 1939). 114 Gravity; Intensities perature, pressure, range of vibration, and associated flexure of the rod supporting the bob of the pendulum.* Thus ab solute gravity is found at secondary base-stations. REDUCTION OF VALUES OF GRAVITY In general, no two gravity stations on land are situated exactly on the same level or equipotential surface. If ob served gravity is to tell us how the density of rock below the earth’s surface is distributed, the observed values of the force must be compared with the theoretical values expected from an assumed figure of the earth. Effective comparison becomes possible when the observed gravity (g) at each sta tion is “reduced” to the value it would have at the actual geoid. The difference between the reduced value and the “theoretical” value, that is, the value (70) expected on the spheroid of reference at the latitude and longitude of the sta tions, is called a “gravity anomaly.” From the sizes and distribution of such gravity anomalies, much can be learned about mass anomalies in the different sectors of the earth. However, the information on this subject varies with the assumptions on which reductions are based. The more important modes of reduction to the geoid are: (1) the free-air reduction; (2) the Bouguer reduction; and (3) various isostatic reductions, each based on particular assumptions. These will be briefly considered in connection with values of gravity at land stations, and afterwards at marine stations. F r e e -a ir R e d u c t io n . If the earth were spherical, the purely gravitational force (g0) acting on one gram of matter at sea level would be (R + h)2/R 2 times the force (g) acting on the same unit of mass at a point h units of length above sea level, R being the radius of the earth. The earth is so * A good summary of this subject is given by C. H. Swick, Bull. 78, Nat. Re search Council, 1931, p. 151, Gravity; Intensities 115 nearly spherical that we can write an approximately exact equation: go l + ™ +h-. (5) S ^ R ^ R 2 If h is less than 6,000 meters, the third term is small enough to be negligible, and g0 — g may be taken as equal to +2gh/R, or 0.0003086 X h gals or 0.3086/2 milligals, where h is expressed in meters. For example, the corrections at sta tions with heights of 100, 500, and 1,000 meters are respec tively + 30.9, + 154.3, and + 309 milligals. For points below sea level, as along the shore of the Dead Sea, go — g is negative. The process of finding from observed gravity the local in tensity of the force at the geoid or other level chosen for com parison of intensities is called the free-air reduction. This assumes that the topography under a normal continental station has no mass, or, in other words, that the space be tween sea level and the measuring instrument is filled with air, a negligible mass, instead of rock; hence the name for this type of reduction. In effect we have a kind of isostatic reduction, founded on the extreme, arbitrary assumption that the topography under the station is compensated en tirely at sea level. To reduce to the geoid the value of gravity (g) observed in a submarine h meters below sea level (see chapter 9), the negative term —2gh/R, analogous to the free-air correction for a land station, must be added. A second but positive term is added to represent the vertical attraction of the layer of water above the measuring apparatus at the time of observation. This term reads:
, 3 D g h + 2 ' A R ’ where D represents the density of the water and A the mean density of the earth. Moreover, there is a third correction, 116 Gravity; Intensities in amount equal to the second, to allow for the fact that the same layer of water would add its own vertical attraction. Hence the value of gravity at the geoidal level (g0) is or
At sea stations this composite correction amounts to 1 milligal for approximately 4.5 meters of submergence at the time of observation.* In practice the ship is sunk to a depth no greater than about 80 meters. B o u g u e r R e d u c t io n . At a point on the geoid and verti cally below a land station, the value of gravity (g" 0) is smaller than the value at the station by the upward attrac tion of the rock above the geoid. Bouguer was one of the first to estimate the amount of this difference at actual sta tions, and therewith opened the way toward a valuable test of the theory of isostasy. That pioneer is memorialized in the name of the mode of reduction now to be described. Bouguer was making observations on the high and exten sive plateau around Quito in South America. He saw it easy to calculate the approximate value of the gravitational pull exerted by the rock between geoid and surface of the ground, if the density (d) of the rock is known. An approxi mate value can be obtained by assuming that the material between geoid and station level has the form of a uniformly thick, plane plate, extended in all directions from the station. The vertical attraction (A) of such a plate is given by the expression 2irkdh, where k is the gravitational constant. The whole vertical attraction (g) at the station is approxi mately UkAR. Hence to the same approximation * A milligal is a thousandth of a gal, which may again be defined as the accelera tion of a mass of one gram by a force of one dyne acting for one second. Gravity; Intensities 117
2irk = 3g A 3>dhg 2A R’ and i Kr Combining this result with the term found in the free-air reduction, we have, for the Bouguer correction in its original form (land stations): _ 2 hg Mhg 2 he. ( M \ g °~ g~ ll~ 2AR~ T (7) So far, then, the Bouguer correction is the free-air correction with one term added. Taking d at 2.67 and A at 5.52, g"0 — g comes out at nearly 1 milligal for 10 meters of height above sea level. If, instead of the infinitely extended plate, there be as-
F igu re 23. The method of making an orographic correction. sumed a circular, plane plate of similar density and thick ness, centering at the station and 100 miles or 160 kilometers in radius, the computed value of g"0— g is nearly un changed. Nor is its value much changed if the plate be supposed to follow the curvature of the earth. On the other hand, an additional and more important cor rection is needed when the station is located in the midst of rugged topography, as exemplified in Figure 23. If the sta tion is on a summit (Si), the allowance for the attraction of the rock between station and geoid is too great by the amount of the vertical attraction that would be exerted at the station by the rock required to fill all adjacent valleys up to the station level (Z,i). If the station (S2) is at the bottom of a valley, a correction is needed because the attrac 118 Gravity; Intensities tion of all rock higher than the station (dotted area of Figure 23) was neglected during the too-simple calculation so far described. In each of the two cases a correction term with positive sign must be added. This “orographic” or “land scape” (German, Gelandereduktion) correction is often desig nated by the symbol (g' — g). For stations on dominating mountains, (g' — g) may reach notable amounts; for exam ple, 48 milligals at Pikes Peak, Colorado, and 123 milligals at the top of Mont Blanc. When the orographic term is added, we have what has been alternatively called an “extended” (Heiskanen) for mula for the Bouguer reduction, with
The difference between g"0 and y0, the theoretical value of gravity at the sea-level point vertically below the station, is a Bouguer anomaly, more useful than that based on the older reduction which ignores the irregularities of topog raphy. The improved formula for calculating the Bouguer anomaly is, then: g"o - 7.) = g + ^ 1 - + (g' - g) - To- (8) In practice the investigator has, of course, to decide on a limit for the radius of the uniform plate, a radius which shall be convenient and at the same time sufficient to ensure es sential accuracy in the final result. A quotation from Vening Meinesz illustrates further how the method is now being applied in comprehensive re searches. 5 The value of this field of anomalies lies in the fact that it gives a complete representation of all the anomalous masses in the up per layers of the Earth. It may be used in studying isostasy, as it demonstrates clearly the effect of the compensating masses and so in many instances it may serve for getting an idea of the way in which the compensation is realized. . . . Gravity; Intensities 119
In order to make these modified Bouguer anomalies better rep resentative of the anomalous masses in the area of the station, the gravity results . . . have been freed, as well as possible, from the effect of anomalous masses in other parts of the Earth, by correcting them for the complete topography and compensa tion of all the numbered zones of the Hayford-Bowie system [see the next chapter]. This way of doing presumes that, roughly speaking, isostasy is valid for most parts of the earth. This assumption seems reasonable because all the present data point towards the truth of it. The modified Bouguer reduction, used by Vening Meinesz, therefore “consisted of a topographic reduction for the zones A — O and an isostatic reduction—according to the regional system—of the zones 18 — 1.” The bounding, circular line separating zone 0 and zone 18 has a radius of 166.7 kilometers.* As in the case of a land station, the calculation of the modified Bouguer anomaly for a station at sea is based on the arbitrary assumption that compensation for topography is completely lacking, or, otherwise expressed, that the ocean floor is underlain by rock of the same density (2.67) as that of the average surface rock of the continents, and is held down by the strength of the earth’s body. In this suppositi tious case, gravity at sea level above the point of observa tion would exceed the value bearing the corrections already made, by the amount of the vertical attraction of a layer of material as thick as the ocean is deep at the station, and with the density of (2.67 — 1.03 =) 1.64, the density of sea water being taken at 1.03. The vertical attraction of the hypothetical layer is given by the expression
3 T64 g T 2 ‘ A R’ * The United States Coast and Geodetic Survey now computes the Bouguer anomalies on the same assumptions, thus saving much extra work with the maps while incurring no errors of moment. The limits of the lettered and numbered zones are given in Table 14, page 141. 120 Gravity; Intensities where T is the thickness of the layer. By so much would this reduction, analogous to the original Bouguer reduction for a land station, increase the value of gravity at sea level. Restricting the described effect to the circular area extend ing 166.7 kilometers (outer limit of the Hayford-Bowie zone O) in all directions from each sea station, Vening Meinesz obtained his “modified-Bouguer” anomalies. The Bouguer anomalies for stations in continental areas are, of course, highly variable from station to station, but in general they are strongly negative. Over the deep oceans these anomalies run from 200 to 400 milligals and are strongly positive. According to Vening Meinesz, these facts give “perhaps the most convincing evidence of the presence of compensating masses that has yet been pub lished.” Clearly the ocean floors are not held down, and the land surfaces in general held up, merely or largely by the strength of the earth. Isostatic Reductions. The Bouguer reduction takes no account of the horizontal and vertical variations of den sity below the geoid. Experience shows that great errors, occasioned by this neglect, may be annulled when isostasy is assumed. A general formula for the force of gravity (gIS0) at sea level below a land station, as calculated after allowance for compensation of the relief, may be written:
giso = g + + A + B, where g is observed gravity; the second term represents the free-air reduction; A is the vertical component of the attrac tion exerted by the material above sea level; and B is the vertical component of the gravitational effect of the corre sponding compensation. The A term includes an improved Bouguer correction and an orographic correction, each of these being ideally applied to the whole extent of the curved Gravity; Intensities 121 earth. In general, for stations on a continent, A has the negative sign and B the positive sign. Thus an isostatic reduction combines three different “corrections.” Heiskanen and other European investigators reduce to the geoid and obtain an isostatic anomaly to be written giso — Jo* The officers of the United "States Coast and Geodetic Survey calculate the theoretical value (gc) of grav ity at the level of the station, and express the isostatic anomaly as g — gc. For any given station, giso — ya = g — gc. In recent Survey publications the symbol yc is used in place of the synonymous gc. The size of the isostatic anomaly varies with assumptions as to the distribution of the compensation for topography. The leading assumptions are embodied in five different hy potheses: (1) the Hayford-Bowie hypothesis, a specific form of Pratt’s idea of compensation; (2) the Airy hypothesis as now usually phrased; (3) the Heiskanen or modified Airy hypothesis; (4) the Putnam hypothesis; and (5) the Vening Meinesz hypothesis. Each hypothesis has variants, match ing differently conceived values for the depth, as well as horizontal distribution, of the compensation around each station. (1) The premises and computing methods used by Hay- ford and Bowie in applying their form of the Pratt explana tion of the earth’s relief will be detailed in chapter 6. (2) Heiskanen has made the first extensive application of the Airy hypothesis.6 It may be recalled that in modern phrasing Airy’s word “crust” is replaced by “sial,” symboliz ing the relatively light rocks at the earth’s surface, and that “sima” conveniently symbolizes the denser rock in which the “roots,” great masses of sial, are buoyed up. Heiskanen made the hypothesis concrete by assuming definite thick nesses for the sial where its upper surface is exactly at sea level. He supposed the densities of sial and sima, respec * Here the departures of the geoid from the spheroid of reference are ignored. 122 Gravity; Intensities tively uniform by hypothesis, to differ by fixed amounts, specifically 0.2, 0.3, and 0.6. Incidentally, the change from one to another of these values was found to have compara tively small effect on the calculated intensity of gravity at a station. With any one of the three figures for the excess of density of the sima, it was easy to compute the thickness of the sial where its surface does not coincide with sea level. Heiskanen’s work was facilitated by the use of elaborate tables giving the original Hayford-Bowie corrections for topography and isostatic compensation at distance from each station. All that was necessary was to compute the factors by which the respective values in those tables should be multiplied, in order to give the values expected from any definite form of the Airy hypothesis. Thus new tables could be drawn up for world-wide use.* (3) However, Heiskanen was led to develop his own idea of isostatic compensation, here called the Heiskanen hypoth esis. He was conscious of the error involved in postulating uniform density for either sial or sima. He accepted the seismological evidence for the existence of discontinuities in the lithosphere, and also used H. Washington’s (albeit ques tionable) data on regional variation of density in the “earth’s crust.” Other assumptions were: (1) that the surface den sity of the sial decreases with the height of the topography above sea level, at a rate which is simply related to that height; (2) that heights of 0, 1, 2, and 3 kilometers corre spond respectively to surface densities of the underlying columns at 2.76, 2.74, 2.72, and 2.70; (3) that the density of the sial increases with depth at the rate of 0.04 for every 10 kilometers of increase of depth; and (4) that the density of * Such tables were published by W. Heiskanen in the Bulletin geodesique of the Union geodesique el geophysique Internationale, No. 30, 1931, p. 87; there the sea- level thickness of the sial was successively assumed to be 40, 60, 80, and 100 kilometers. In 1938 he issued (Annales Acad. Sci. Fennicae, ser. A, vol. 51, No. 9) new, slightly more accurate tables for the factors, with sea-level thickness of the sial taken successively at 20, 30, 40, and 60 kilometers. Gravity; Intensities 123 the sima increases more slowly, being 3.06 at the depth of 10 kilometers below the Pacific water and 3.14 at a level 40 kilometers deeper. (See Figure 24, copied from Heiskanen’s own drawing.)7 (4) Putnam regarded the kind of isostatic compensation assumed by Hayford and Bowie as “inconceivable; it could
Figure 24. Heiskanen’s section illustrating his hypothesis of isostatic compensation. only be obtained if the material were so plastic that no sur face irregularities would remain.” Putnam proposed a spe cial form of “regional isostatic reduction” and illustrated it in the case of a mountainous region. (See Figure 25.) He imagined a leveling-off of all the topography around each station: first, to a radius of 37 miles from the station (the limit of zone M in Table 14), and then to a radius of 104 miles (the limit of zone 0 in Table 14); and he assumed compensa 124 Gravity; Intensities tion for such imagined topography. After allowance for the vertical components of the “average-level” topography and for its isostatic compensation, he obtained an “average- level anomaly” for each station. In nearly all cases the local anomaly is algebraically larger when the station is above the general level, approximately in propor-
STATION
... AVERAGE LEVEL —< REGIONAL — | L O C A L __i S e a /e v e ! he------ZONE L IM IT S ------H
Figure 25. Putnam’s section illustrating three modes of isostatic compensation. tion to the elevation difference, and is smaller in similar propor tion when the station is below the general level; in 44 compari sons with zone M anomalies there are only 6 which as to sign are at variance with this. As the local anomaly should be larger for the “above” stations, and smaller for the “below” stations, it is reasonable to ascribe these systematic differences also to error due to a reduction based on complete local compensation. . . . A reduction using limited regional compensation will give anomalies nearer the truth in mountainous regions than one with
BOUGUER FREE-AIR PUTNAM Figure 26. Putnam’s sections illustrating three modes of reduction, the station being above the general level of the topography. a complete local compensation. Such a distribution may be represented as the compensation required by topography bounded by the warped surface lying between the earth’s surface and the average level in any region.8 Figures 26 and 27 are copies of Putnam’s sections illus trating his comparison of the free-air and Bouguer reductions with his isostatic, average-level reduction. The station is Gravity; Intensities 125 at the point S. The rock above sea level is indicated by vertical shading; the isostatic compensation for the topog raphy by horizontal shading. It will be noted that, for the station above the general level, the width of the band of horizontal shading is zero in the case of the Bouguer reduc tion (no compensation); that the band is relatively wide in the case of the free-air reduction (overcompensation); and that the corresponding band is narrower in the case of the average-level reduction, with the compensation represented as the negative attraction of a plate of the same density as the topography. For a station below the general level, the
AVERAGE
S ea - illiliiffliil le v e l
BOUGUER FREE-AIR PUTNAM Figure 27. Putnam’s sections illustrating three modes of reduction, the station being below the general level of the topography. graph illustrates the undercompensation necessitated by the free-air mode of reduction. Figure 27 is Putnam’s graphic illustration of the rear rangement of topography involved if average-level or, alter natively, regional compensation be assumed in place of local compensation. The actual compensation, which is a defi ciency of density extending a considerable distance below sea level, is not indicated.* (5) The Vening Meinesz regional form of the isostatic theory was described by this authority in the Bulletin geo- * See G. R. Putnam, Proc. Nat. Acad. Sciences, vol. 14, 1928, p. 413. When, in 1895, Putnam applied his “average-elevation isostatic reduction” (involving regional compensation) to observations at 25 stations in the United States, he regarded his result as a proof of isostasy in that country. He later (Nature, February 23, 1929) described it as “the first consistent proof of isostasy,” and pointed out that his method of testing isostasy does not depend on “any assump tion as to the thickness or vertical density arrangement of the compensation, pro viding it is at a considerable depth.” Such assumptions are essential in the Hayford-Bowie method of testing isostasy, but the results of applying this method also show that the compensation is regional (see G. R. Putnam, Bull. Geol. Soc. America, vol. 33, 1922, p. 299). 126 Gravity; Intensities desique of the Union geodesique et geophysique internationale, p. 3 (1931). Translated, his statement reads: The method is based on the hypothesis that one can consider topographic masses situated above sea level as having been added to the earth’s crust, and that the crust yields under their weights and is therefore depressed into the subjacent couche of viscous liquid which supports the crust, the depression continuing until hydrostatic balance is re-established. It is clear that this hy pothesis does not well represent the way in which the tectonic forces have given birth to mountains or the method by which continents and oceans have been formed, but it probably gives a sufficiently exact idea of the effects of erosion and sedimenta tion. Those processes have caused deformation of the earth’s surface, and erosion is the primary cause of local irregularities in topography. For a large part of the local relief of the earth the hypothesis gives an acceptable approximation to the truth. We shall suppose that the terrestrial crust reacts to the added weights on the surface like a plate of indefinitely great extension and of constant thickness—a plate obeying the laws for elastic solids and floating freely on a liquid layer of higher density. These properties are certainly not exactly represented in Nature, but there is reason to believe that they do not differ too much from the truth. It may be remarked that, since we are studying a problem in statics, the viscosity of the liquid couche plays no role. The property that seems most doubtful is the constancy of thickness. Vening Meinesz then proceeds to show that his method of reduction gives useful results, whether the density of the “crust” be supposed uniform or, as more in accord with probability, be thought to increase with depth from the surface. His idea is thus a crust-bending or crust-warping hy pothesis, much like that independently worked out by Glennie (see chapter 8), and really involves the postulate of buoyant support for high topography by “roots.” Indirect Reduction. Even under isostatic conditions the geoid undulates, with small amplitudes, across the Gravity; Intensities 127 spheroid of reference. There is rock matter or lack of mat ter between the two surfaces, and the positive or negative attraction of this material or lack of material is not allowed for during the computation of the ordinary isostatic an omaly. Hence in general a small correction is needed; this is obtained by the so-called “indirect reduction.” In land areas the indirect correction to the ordinary iso static anomaly is always positive, as may be seen in examples given in Part 4 of “Principal Facts for Gravity Stations in the United States,” issued by the United States Coast and Geodetic Survey. There values of the indirect anomalies are stated for stations 714 to 925 inclusive. The computa tions were made on the basis of the International spheroid, with depth of compensation at 96 kilometers. Table 13 in cludes the results for 11 stations, chosen so as to include those with heights above sea level respectively near the maximum and minimum for the whole list in Part 4, but otherwise chosen at random. The indirect anomaly is algebraically larger than the Hayford anomaly by 2 to 5 milligals.* For all 212 stations listed in Part 4 the mean indirect- isostatic anomaly is only 2.8 milligals larger (algebraically) than the Hayford anomaly computed to the geoid.f In general the difference is too small to be important in geo physical problems. For example, Heiskanen states that the geoid under the axis of the Swiss Alps is no more than 5 to 10 meters above the geoid in Bavaria or Lombardy, and, more * The tables for determining the form of the geoid and its indirect effect on gravity were prepared by W. D. Lambert and F. W. Darling (Special Publication, U. S. Coast and Geodetic Survey, No. 199, 1936). t Since Table 13 and accompanying text were prepared, the Survey has issued (in 1940) Part 5, giving data for stations 926 to 1,081. They show an average indirect anomaly which is 3.5 milligals larger than the average Hayford (96 kilo meters) anomaly. The corresponding average difference for all 368 stations, 714 to 1,081, is 3.1 milligals. The maximum difference is 6 milligals; the minimum, 2 milligals. E. C. Bullard (Phil. Trans. Roy. Soc. London, vol. 235A, 1936, p. 493) found the excess of the indirect anomaly at a high station in East Africa to be 4 milligals. 128 Gravity; Intensities recently, Niethammer reports, for the St. Gothard section, 2.3 meters as the maximum deviation of the actual geo id from the spheroid.9 The deviation does become important in fixing the amount and even the sign of the small mean anomaly over the wide ocean. At a sea station the indirect correction increases theoretical gravity and therefore causes an algebraic decrease in the anomaly. This last-mentioned fact goes far toward explaining why the small, average Hay-
T able 13 COMPARISON OF HAYFORD AND INDIRECT-ISOSTATIC ANOMALIES
Hayford Indirect-isostatic Station Locating Elevation anomaly anomaly number State (meters) (milligals) (milligals) 714 Louisiana 5.8 -30 -27 721 Texas 651 -39 -35 735 Alabama 21.5 -4 0 -38 758 Texas 1,291 + 12 + 16 766 New Mexico 1,655 +20 + 25 767 New Mexico 1,323 -21 -16 770 Arizona 1,291 -11 - 6 789 Massachusetts 23 -12 - 9 811 New Jersey 370 -32 -29 854 North Carolina 5 -22 -20 889 Florida 3 -16 -13 ford anomaly found by Vening Meinesz along' his trans pacific line of stations has the positive sign. The problems discussed in this book seem not to be spe cially illuminated by some other kinds of reduction, includ ing those of Helmert, Brillouin, Rudzki, Prey, and Jung. Good summaries concerning their nature appear in chapter 42 of the “Ilandbuch der Geophysik,” edited by B. Gutenberg (vol. 1, Berlin, 1936), the chapter being written by W. Heis- kanen; and in K. Jung’s paper, “Ueber vollstandig isostatische Reduktion,” in the Zeitschrift fiir Geophysik, vol. 14, 1938, p. 27. Gravity; Intensities 129 A CLEARING-HOUSE FOR SYSTEMATIC RECORD OF ANOMALIES Values of gravity at more than 5,000 stations have been reported, many of them without isostatic reduction. The isostatic anomalies actually published are based on different assumptions about compensation, on computational meth ods of unlike precision, and on different spheroids of refer ence. All these variations of procedure make it more diffi cult to compare, and to discuss the true meaning of, the anomalies. And a less excusable trouble is due to a rather common failure of the investigators to accompany their lists of isostatic or other anomalies with easily found state ments concerning the spheroidal figure from which the re spective anomalies were calculated. Fortunately, these seri ous handicaps for the student of earth physics have been largely removed since the International Association of Geod esy established a clearing-house, its “Isostatic Institute,” headed by W. Heiskanen of Finland.10 Under his direction full data for some 3,500 stations, including all the important kinds of anomaly, have already been worked out, the reduc tions throughout being based on the same formula—the 1930 International formula—for the standard spheroid. Another useful product of the Isostatic Institute is the publication of world maps which, it is hoped, will be allowed to speed up and make more accurate the work of computing the topographic-isostatic effects of the Hayford zones 1 to 10 (see Table 14).11 Similar maps for zones 11 to 13 inclusive are planned, the inner limit of zone 13 taken at only 380 kilo meters from the station. References
1. A. E. Benfield, Z eitf. Geophysik, vol. 13, 1937, p. 157. 2. See W. D. Lambert, “The Figure of the Earth” (Bull. 78, National Research Council, Washington), 1931, pp. 136-7. 130 Gravity; Intensities 3. A. Schleusener, Zeit. f. Geophysik, vol. 8, 1934, p. 389. H. Haalck, ibid., vol. 8, 1932, pp. 17, 197; vol. 9, 1933, pp. 81, 285; Beitraege zur angewandten Geophysik, vol. 7, 1938, p. 285. F. Holweck and P. Lejay, Comptes Rendus, Acad. Sciences, Paris, Jan. 3, 1933. G. Norgaard, Geodaet. Inst., Copenhagen, Meddelelse No. 10 and No. 12, 1939. 4. See F. Kiihnen and P. Furtwangler, Bestimmung der abso- luten Grosse der Schwerkraft zu Potsdam mit Reversions pen- deln, Berlin, 1906. 5. F. A. Vening Meinesz, “Gravity Expeditions at Sea,” Delft, 1934, vol. 2, p. 30. 6. See W. Heiskanen, Verofft. Finnischen Geodat. Institutes, No. 4, 1924, p. 15, and other references to his writings given in chapters 6 and 7. 7. W. Heiskanen, Annales Acad. Sci. Fennicae, ser. A, No. 6, 1932, p. 6. 8. G. R. Putnam, Proc. Nat. Acad. Sciences, vol. 14, 1928, pp. 408, 417. 9. W. Heiskanen, Gerlands Beitraege zur Geophysik, vol. 36, 1932, p. 194; T. Niethammer, Bull. 20, Schweiz. Geodat. Komm., 1939. 10. See a paper by W. Heiskanen in the Comptes Rendus of the tenth session of the Baltic Geodetic Commission, 1938, p. 98. 11. See W. Heiskanen and U. Nuotio, Annales Acad. Sci. Fen nicae, ser. A, vol. 51, No. 11, 1938. 5 GRAVIMETRIC TEST OF ISOSTASY IN THE UNITED STATES, BY HAYFORD AND BOWIE
INTRODUCTION The first systematic attempts to deduce from observed values of gravity the degree of isostasy in the United States were made by the national Coast and Geodetic Survey. Even before Hayford’s second report on deflections of the vertical was published, Hayford and his colleague, Bowie, had begun to develop an adequate network of gravity sta tions. The results from 89 stations and the method of rea soning from the observations there made were detailed in Special Publication No. 10 of the Survey, with the title “The Effect of Topography and Isostatic Compensation upon the Intensity of Gravity,” by J. F. Hayford and W. Bowie (Washington, 1912). This quarto volume will be referred to as Report “X.” Also in 1912 the Survey issued Special Publication No. 12 (symbol “XII”) by W. Bowie, dealing with 35 additional stations, or 124 in all. Five years later Bowie published Special Publication No. 40 (symbol “XL”), covering 219 stations in the United States and discussing analogous data from 42 Canadian stations, 73 Indian stations, and 40 other stations, principally in Europe. In 1924 the same author published Special Publication No. 99 (symbol “IC”), cover ing 313 stations in the United States. 131 132 Gravimetric Test oe Isostasy All four investigations were based upon assumptions sub stantially like those made in the 1909 and 1910 reports on the deflections of the vertical. It will be convenient to re view the general argument contained in the first of the 1912 reports (symbol, “X”), and afterwards to consider the re sults of the later researches. There will be some repetition of statements of principle, partly to ensure that direct quota tions from the reports shall faithfully set forth the reasoning of the authors. After defining isostasy, Hayford and Bowie gave mathe matical expression to that particular form of the hypothesis which, though known at the outset to be incorrect, seemed best fitted to provide a practical, quantitative test of the hypothesis. The type of isostasy assumed may be under-
Figure 28. Hayford-Bowie sections illustrating the Pratt-Hayford compensation, reckoned from sea level and also from the rocky surface. stood by referring to Figure 28, which shows the general re lations of density supposed to rule in the earth’s outer shell. ASSUMED CONDITIONS FOR ISOSTATIC COMPENSATION Let h represent the depth of compensation, measured from sea level and assumed to be constant; and let D represent the mean surface density of the solid part of the globe. Gravimetric Test of Isostasy 133 Then the mass of matter in a column of unit area at the sea- coast is Dh. Let H represent the height of the top of an inland column above sea level, the mass of this column above sea level thus being DH. If the density of that portion of the inland col umn which extends from sea level down to the depth of com pensation is d, then the mass of matter in the whole column, including the part above sea level and the part below it, equals DH + dh. By definition, at the depth of compensation any element of mass is subject to hydrostatic pressure, and to a close approximation this would be true if the masses of the various unit columns are identical, or D ll + dh = Dh. ( 10) From equation (10) it follows that , _ D(h~ II) (ID The difference, E i, between D and d is expressed by the equation D (h - II) E l = D - (12) h This difference between the normal density at the surface of the land and also throughout a column at the seacoast on the one hand, and the density of an inland column below sea level on the other, is the average compensating defect of density, and this difference multiplied by the depth of com pensation is the compensating defect of mass, E-Ji. The total mass in the inland column may also be expressed by the equation (see Figure 28): Mass in any land unit column = D ll + Dh — E\h. (13) As the mass in each unit column is the same, DII = E xh. Thus, in each unit column the compensating defects of mass below sea level are equal to the mass above sea level which 134 Gravimetric Test of Isostasy is considered to be the surface excess. Equation (12) states that the compensating defect of density is proportional to the elevation of the surface above the sea level, as D and h are assumed to be constant. In an ocean column let Z represent the depth of water, the density of which is A. The depth of the solid part of the column is h — Z\ the density of this part will be called S. Then the mass of matter in the column is A Z + 8 (h — Z), which, by definition, equals Dh. It follows that „ Dh — A Z The difference, E 2, between the density of the solid part of the ocean column, 8, and the normal density, D, is ex pressed by the equation Dh — b.Z E 2 = h - Z (D - A) Z or E 2 = (14) h — Z ' The total mass in any ocean column may also be expressed (see Figure 28) as AZ + ( D + E 2)(h - Z). (15) As the mass in each unit column is the same, namely Dh, it follows that Z{D — A) = E 2 (h — Z). That is, in the solid part of each ocean unit column the compensating ex cess of mass is equal to the defect of mass in the water part of the column. Equation (14) indicates that the compensating excess of density is nearly proportional to the depth of water, as D and A are assumed to be constant and (h — Z) is approximately constant. Hayford and Bowie adopted 2.67 as the mean surface density of the solid part of the earth, and 1.027 as the density of sea water. With these values D — A = 0.615 77. Hence for oceanic unit columns we have 0.615 Z E 2 = D (16) h - Z ' Gravimetric Test of Isostasy 135 As a concrete illustration, consider the three unit columns of Figure 28, A. One column is beneath a mountain summit at an elevation of 3 (= H) kilometers; a second is topped at sea level; the third is topped 5 (= Z) kilometers below sea level. The depth of compensation is assumed to be 114 (= h) kilometers below sea level. In the first column the ratio of H to h is 3/114 and the defect of density (A/) is 3/114 of 2.67, or 0.07. In the second column the density of the material is 2.67. In the third column the compensating excess of density (£2) of the rock underlying the ocean is by equation (16) equal to D X (5 X 0.615)/(114—5) or 0.075; here, then, the density of the material is 2.745. Under the mountain the average density is about 3 per cent less than under the seacoast, where the density is about 3 per cent less than under the ocean with depth of 5 kilo meters. On p. 9 of Report X we read: If the condition of equal pressures, that is of equal superimposed masses, is fully satisfied at a given depth, the compensation is said to be complete at that depth. If there is a variation from equality of superimposed masses, the differences may be taken as a measure of the degree of incompleteness of the compensation. In the above definitions it has been tacitly assumed that g, the intensity of gravity, is everywhere the same at a given depth. Equal superincumbent masses would produce equal pressures only in case the intensity of gravity is the same in the two cases. The intensity of gravity varies with change of latitude and is subject also to anomalous variations which are to some extent associated with the relation to continents and oceanic areas. But even the extreme variations in the intensity of gravity are small in comparison with the variations of density postulated. The extreme variation of the intensity of gravity at sea level on each side of the mean value is only 1 part in 400. Even this small range of variation does not occur except between points which are many thousands of kilometers apart. As will be shown later, the postulated variations in mean densities are about 1 part in 30 on each side of an average value. Hence, it is not advisable to complicate the conception of isostasy and 136 Gravimetric Test of Isostasy introduce long circumlocutions into its definition in order to introduce the refinement of considering the variations in the intensity of gravity. The variation of the intensity of gravity with change of depth below the surface need not be considered, as its effect in the vari ous columns of material considered will be substantially the same.* The idea implied in this definition of the phrase “depth of compensation”, that the isostatic compensation is complete within some depth much less than the radius of the earth, is not ordinarily expressed in the literature of the subject, but it is an idea which it is difficult to avoid if the subject is carefully studied from any point of view. (Report X, p. 9.) The assumed depth of compensation, 113.7 kilometers, was the best available at the time the computation of the gravity reduction tables . . . was commenced. A better value, 122 kilometers, became available while these computations were in progress, but too late to be used. (Report X, p. 10.) So far, the isostatic compensation has been assumed to extend everywhere to a uniform depth below sea level. Dur ing the actual computations, the compensation was assumed to extend everywhere to the depth of 113.7 kilometers, meas ured downward from the solid surface of the earth. See Figure 28.f For land areas, in computing the direct effect of the topography, the rock above sea level was assumed to have the density D, but in computing the effect of the com pensation the density was assumed to be D — E i above sea level as well as below. In computations for oceanic com partments formula (16) becomes E2 = DX 0.615 Z/h. (17) * E. C. Bullard (Zeit.f. Geophysik, vol. 10, 1934, p. 318), found that “the outer zones in the Hayford-Bowie tables require corrections up to 200 per cent, to allow for the variation of gravity with depth.” However, since the net effect of the outer zones is small, the Bullard correction is also small. t E. C. Bullard (Phil. Trans. Roy. Soc. London, vol. 235A, 1936, p. 491) has shown that correction for compensation is facilitated, without loss of accuracy, by taking the depth of compensation at a fixed distance from sea level rather than at a fixed distance from the rocky surface. Gravimetric Test of Isostasy 137 The compensation was assumed to be everywhere uni formly distributed with respect to depth. Thus, the com pensating defect or excess of density under a given land or sea area was supposed to be, at all depths less than the depth of compensation, respectively equal to the E x and E 2 of equations (12) and (14). In the principal discussion the compensation was assumed to be complete under every part of the earth’s surface, how ever small. We read: The authors do not believe that any of these assumptions upon which the computations are based is absolutely accurate. The mean surface density is probably not exactly 2.67 and the actual surface density in any given area probably does not agree exactly with the mean. The depth of compensation is probably not ex actly 113.7 kilometers, and it probably is somewhat different under different portions of the earth’s surface. The compensa tion is probably not distributed uniformly with respect to depth. It is especially improbable that the compensation is complete under each separate small area, under each hill, each narrow val ley, and each little depression in the sea bottom. . . . The authors believe that the assumptions on which the com putations are based are a close approximation to the truth. They believe also that the quickest and most effective way to ascertain the facts as to the distribution of density beneath the surface of the earth is to make the assumptions stated, to base upon them careful computations for many observation stations scattered widely over the earth’s surface, and then to compare the computed values with the observed values of the intensity of gravity in order to ascertain how much and in what manner the facts differ from the assumptions. In this investigation, accordingly, the intensity of gravity at many observation stations has been computed on the assump tions stated. These computed values have been compared with the observed values at these stations. The differences between the observed and computed values, the residuals, are due to two classes of errors. In the first class are errors in the observations and computations. In the second class are errors in the assump tions. The average and maximum magnitudes of the errors of the first class are fairly well known. The magnitude and char 138 Gravimetric Test of Isostasy acter of the residuals which may be produced by them are fairly well known. It is shown in this publication that the residuals, differences between observed and computed values of the in tensity of gravity, are larger than may be accounted for by the first class of errors. Therefore it is certain that the second class of errors are of appreciable size. In other words, it is certain that the assumptions are appreciably in error. But, as the residuals are but little larger than may be accounted for by the first class of errors, it is certain that the assumptions are nearly correct. The residuals contain evidence not only as to the extent but also as to the manner in which assumptions depart from the truth. To read and interpret this evidence precisely is exceed ingly difficult because of the fact that the residuals are small. If the residuals were large, it would be clear that the assumptions were far from the truth, and it would be easy to see in which di rection the truth lay. In the actual case it is difficult to ascer tain in what way the assumptions should be changed to make them a closer approximation to the whole truth, while still re maining a statement of general laws applicable to the whole United States.* (Report X, pp. 11, 12.) We saw that deflections of the plumb line can be compared and made geophysically useful only when referred to a defi nite figure of the earth. So it is here also; to discern hori zontal variation of rock density from the intensities of grav ity at many stations, all the observed values must be reduced to an assumed common spheroid, temporarily chosen as “standard.” When Report X was being prepared, the best available spheroid was thought to be that derived by Hel- mert from data supplied by stations in many countries, chiefly those of the Old World. This formula was proposed in 1901 and was based on a measured value of absolute grav ity at a point in Vienna, that is, on the “Vienna system.” It reads: 70 = 978.046 (1 + 0.005302 sin2 - 0.000006 sin2 2), where 70 is the force of gravity at a given sea-level * In this passage “residual” is a synonym for “anomaly,” a word now preferred when reference is made to difference between observed and computed values of gravity Gravimetric Test of Isostasy 139 point, and 978.046 represents the force at the equator and at sea level; the force is expressed in dynes or the numeri cally equivalent gals (centimeters per second per second or cm/sec2); and 4> is the latitude of the station. (See also Table 2, p. 31). It will be noted that circularity for each parallel of latitude is assumed. If the absolute value of gravity at Potsdam had been taken as the basis, the constant factor, 978.046, would have to be changed to 978.030, leaving the expression within the brack ets unchanged. The reference to Potsdam became possible after G. R. Putnam had swung a pendulum at Potsdam and at Washington, whereby gravity at a certain point in the city of Washington, measuring 980.111 gals, could be re garded as “absolute.” In this way Washington was made the base for reduction of observations all over the United States. THEORETICAL GRAVITY AT A STATION The reference spheroid represents the value of gravity at sea level on an ideal, utterly smooth earth, with no variation of density along any underground level. Actual measure ments of gravity are made on the real earth, with topo graphic relief and with horizontal variation of density, and in the United States the measurements are of course usually made above sea level. Hence, to reduce the observed values of gravity to a common basis of comparison, those values have to be corrected as follows: (1) for the elevation of each station; (2) for the vertical component of the gravitational pull exerted by the topography of the whole earth; and (3) for the effect of any compensation for the topography, which also has a vertical component. Correction for Elevation. Throughout all of the Hay- ford-Bowie investigations the aim was to find the “theo retical” or “normal” intensity of gravity at the level of the station, not at sea level below the station. If H is the ele vation of the station above sea level, and R is the radius of 140 Gravimetric Test of Isostasy the earth (regarded without essential error as a sphere with radius of 6,370 kilometers), the attraction at the station (g) is to that at sea level directly below the station (g0) as (R - 77)2 is to R2. Thus, g = g0 (1 - 2H/R + H2/R 2). Since H 2/R 2 is in general a negligible quantity, g may be taken as smaller than g 0 by the fraction 277/7? or 0.000308677 dynes, where 77 is expressed in meters. The amount of the diminution is evidently equal to the free-air correction when the observed gravity at the same station is reduced to sea level, but with the sign changed. Compare equation (5), p. 115. C o r r e c t io n fo r t h e E f f e c t s o f T o po g r a ph y a nd C ompensation . Calculation of the influence of topography and its compensation on the gravity at each station is a much more serious matter. As already remarked, the method of attack used by Hayford and Bowie was in principle like that used in the 1909 and 1910 investigations. Here, however, the relief of the whole planet and the compensation for that relief were considered. The terrestrial surface, all the way to the antipodes of the station, was divided into zones by circles, each having the station at its center.* Most of the zones were divided into compartments by radial lines. To make the work easier, the sizes of the zones and compart ments were chosen arbitrarily, but such treatment involved no danger of significant error in the results. The zones limited exteriorly by a radius of 166.7 kilometers were let tered. The remainder were numbered, with radii indicated for convenience in degrees of arc. (See Table 14.) It will be noted that zone A begins at the station, and that zone 1 ends at the antipodes of the station, j * S. G. Burrard (Professional Paper No. 5, Survey of India) had already shown that the topography and compensation as far as at least 4,000 miles from the station somewhat affect both the direction of the plumb line and the time of oscillation of a gravity pendulum. t This zone system for making topographic and isostatic reductions is now in general use, but to ensure greater accuracy the zones lettered C, D, E, F, and O are each subdivided into two sub-zones (see W. Heiskanen, Annales Acad. Sci. Fennicae, ser. A, vol. 51, No. 9, 1938, p. 13). Gravimetric Test oe Isostasy 141
T able 14 ZONES AND COMPARTMENTS Designation Outer radius Number of compart of zone of zone ments in zone A 2 meters 1 B 68 4 C 230 4 D 590 6 E 1,280 8 F 2,290 10 G 3,520 12 H 5,240 16 I 8,440 20 J 12,400 16 K 18,800 20 L 28,800 24 M 58,800 14 N 99,000 16 O 166,700 28 18 1° 41' 13" 1 17 1 54 52 1 16 2 11 53 1 15 2 33 46 1 14 3 03 05 1 13 4 19 13 16 12 5 46 34 10 11 7 51 30 8 10 10 44 6 9 14 09 4 8 20 41 4 7 26 41 2 6 35 58 18 5 51 04 16 4 72 13 12 3 105 48 10 2 150 56 6 1 180 1 For each compartment a “reduction table” was prepared. This table gives the relation between the mean elevation of the ground in the compartment, above sea level, and the effect of the corresponding topography and compensation, on the vertical component of these opposite-sign attractions at the station. The calculation of the tables, for all zones except zone A, was made with the help of formulas which involve: k (the gravitational constant), taken at 6.673 X 10-8 (e.g.s. system); D, the distance of an elementary mass (dm) in the given compartment; /3, the angle of depression 142 Gravimetric T est of Isostasy of the straight line drawn from the station to the elementary mass; 6, the angle at the center of the earth (regarded as spherical) subtended by the straight line between station and elementary mass; and r, the radius of the earth, assumed to be 6,370 kilometers. At the station the vertical component of the attraction of the elementary mass is, expressed in dynes: sin 18 k.dm D2 (18) If the station and the elementary mass are at the same elevation above sea level, (3 = -,e and , D„ = „2r sin . -•e
F igure 29. Attraction of an F igure 30. Attraction of an elementary mass at distance BS elementary mass at distance BS from a station situated on the from a station situated on a same level as the mass. lower level. (See Figure 29.) Hence the vertical component at the sta tion is . e (19) 4, r1 2 sin2 ' 2 -9 Gravimetric T est of Isostasy 143 If the elementary mass is higher than the station by an amount h, the vertical component of the attraction of dm at the station is cos sin — sin + h2 + 2D\h sin - k.dm (20) D\ + h2 + 2Dih sin ^ (See Figure 30.) If the elementary mass is lower than the station by the amount h, the vertical component of the attraction of dm is h cos sin + sin- + h2 — 2D\h sin k.dm — ( 21) D\-\- h2 — 2D\h sin 6 (See Figure 31.) For masses near the station, the formula used was that rep resenting the attraction of a right cylinder upon a particle outside the cylinder and lying in its produced axis. This attraction on unit mass of one gram is equal to k 2 wS [Vc2 + k2 — + (h + t)2 + t], (22) where 8 is the density of the material; c is the radius of the cylinder; t is the length of an F igure 31. Attraction of an elementary mass at distance BS element of the cylinder; and h from a station situated on a is the distance from the attracted higher level. 144 Gravimetric Test of Isostasy point, the station, to the nearest end of the cylinder.* For a cylindrical shell of matter, which may be regarded as the difference of two concentric cylinders of the same length but of different radii, cx and c2, the attraction on one gram, in dynes, is manifestly k2T5[V$+~h* - Vc[+li?- + (23) In the case of a land station, the reduction table for zone A was calculated by formula (22). When the effect of the topography (a vertical cylinder with axis passing through the station) was sought, 8 was assumed to be 2.67; the result was a positive quantity. The effect of the corresponding compensation—a negative quantity—was computed by the same formula, but here 8 was given the value 2.67 X 77/11,- 370,000, H being the elevation of the surface above sea level, in centimeters. The isostatic compensation is thus treated as a cylinder of ma terial of negative density . . . or, in other words, as a negative mass just equal to the positive mass which would exist in this zone above sea level if the actual density of all material in the zone above sea level were 2.67. (Report X, p. 19.) The resultant of the two effects was computed for different values of the elevation of station and compartment, and entered in a reference table, p. 30 of Report X. The effect of topography in zone A under a station at sea is found by taking 1.643 (= 2.67 —1.027) for 8 in formula (22), so as to allow for the defect of density of sea water in comparison with average rock at the earth’s surface, the ratio being as .615 to 1.000. Here h is zero. The effect of the compensation is calculated from the same formula, when for 8 is given the value 2.67 X 0.615Z/11,370,000, Z being the depth of water and h being equal to Z. The * The steps in the integration on which this formula depends are described on p. 47 of J. H. Pratt’s book “The Figure of the Earth,” 4th edition, 1871, as well as in the “Traits de Mechaniqtie Cilesle,” by F. Tisserand, Paris, 1891, vol. 2, p. 71. Gravimetric Test of Isostasy 145 two effects are respectively negative and positive, that is, of sign opposite to that characteristic of the corresponding effects for a land station. For zones B to 0 inclusive, the effects of topography and isostatic compensation were calculated separately, and in both cases by the use of formula (23). The procedure varied in detail according as the station is on, above, or below the level matching the mean elevation of the surface of the zone considered. See pp. 20-2 of Report X. For zones beyond zone O, formulas (19), (20), and (21) were used. The integration required was accomplished by numerical computation. See pp. 23-8 of Report X. It was decided, however, to expedite the calculations by determin ing directly the resultant effect of topography and compensa tion, rather than to find values for the two effects separately. The authors believed that this short cut in method would involve no essential loss of accuracy. Toward the end of the investigation they concluded that, while no vital errors were occasioned, it would have been more illuminating to have computed the effects separately out to at least zone 6. Thus complete reduction tables for all zones, from station to its antipodes, were constructed and published on pp. 30-46 of Report X. The tabulated values represent the vertical components of the attraction of a unit mass at the station expressed in the fourth place of decimals in dynes or gals. As in the investigations of deflection of the vertical, the work of correcting for topography and isostatic compensa tion was facilitated by the use of templates and the principle of interpolation.* On pp. 65-70 of Report X, the authors discuss the change
* E. C. Bullard (Phil. Trans. Roy. Soc. London, vol. 235a, 1936, p. 487) has considerably simplified the method of computing the attractions of topography and compensation, the actual work being much diminished but without any essen tial loss of accuracy in the results. His method is now being used by the United States Coast and Geodetic Survey. 146 Gravimetric Test of Isostasy of sign affecting the resultant effect as the distance from a station increases. We read: This change of sign of the effect, without any change from land to ocean, should be carefully noted and the reasons for it studied, for otherwise one’s general conception of the relations between the topography and isostatic compensation surrounding the sta tion, on the one hand, and the attraction of gravity at the station, on the other hand, is apt to be largely in error. . . . The effect of the topography decreases continuously without change of sign as the distance from the station is increased. This is also true of the effect of the compensation. These two effects decrease according to different laws. At a near station the effect of the topography is very large in comparison with that of compensation. The ratio of the two effects is unity at a dis tance of about 10 kilometers from the station. The ratio con tinues to decrease until it reaches a minimum of about 0.04 at about 139 kilometers (1° 25') from the station. It then increases again to a value (0.99) which is nearly unity at the antipodes. . . . The positive resultant effect . . . decreases very rapidly . . . to zero at a distance of about 10 kilometers where the effects of topography and compensation just counterbalance each other. For all greater distances the resultant effect is negative, the effect of the compensation being greater than that of the topography. Table 15 shows the calculated ratios of the effects at dif ferent distances, in an assumed case where the area of topog raphy is 1 square meter, with surface 5,000 feet above sea level, the station also having an elevation of 5,000 feet. Aside from the unfamiliar change of sign thus far commented upon, due entirely to increase of distance from the station, there is another which occurs at nearly every station due to an entirely different and ordinarily well-recognized cause, namely, the change from land to oceanic zones. Since about three-fourths of the world’s surface is covered with deep oceans, sooner or later, as successively more zones are taken, a zone is reached in which the water in the zone predominates largely over the land. This produces a change in the sign of the resultant effect upon the vertical component of the attraction at the station. . . . In general, therefore, at every station situated on land, as succes- Gravimetric T est of Isostasy 147
T able 15 RATIOS OF EFFECT OF TOPOGRAPHY DIVIDED BY EFFECT OF COMPENSATION
Distance from station Ratio of effects Resultant effect to center of topography (dynes X 10l()) Meters 0 Large +200,000 35 Large +5,000 150 60 + 1,100 940 46 +90 2,900 7 +6 Kilometers 10 1 0 16 .5 -.06 24 .2 -.06 44 .1 -.033 79 .07 -.013 139 (= 1° 25') .04 -.0029 2° 20' .1 -.0008 7 45 .5 -.000024 13 .7 -.000005 29 .93 -.0000005 70 .98 -.00000005 180 .99 -.00000002 sively larger zones are considered, two changes of sign are found —one due simply to increase of distance from the station and one due to a change from land zones to water zones. Bowie himself has supplied a good summary of the situa tion, given on p. 8 of Report XL: In nearly all cases the combined effect of the topography and compensation changes sign from plus to minus before zone L is reached. This zone has an inner limit which is only 19 km from the station. This is an important matter which should be con sidered by anyone studying the question of isostasy and its effect upon the intensity of gravity. Explanation of the change of sign is outlined thus: Near the station the topography has the predominating effect, 148 Gravimetric Test of Isostasy as it is much closer than the center of mass of the compensation. As the distance from the station increases the ratio between the sine of the depression angle to the center of the compensation and the sine of the angle of elevation or depression to the center of the topography becomes greater. At the same time the ratio of the distances to the compensation and to the topography becomes less. Therefore at a certain distance the vertical component of the effect of the compensation becomes greater than that of the topography. It is evident that at great distances from the station the effect of the compensation will be greater than the topography. It should be noted that the effect of topography in the oceans is negative and its compensation positive. This fact causes the combined effect for the more distant zones, which cover water areas mostly, to be positive. In general, therefore, at every station situated on land, as suc cessively larger zones are considered, two changes of sign are found—one due simply to increase of distance from the station and one due to a change from land zones to water zones. Hayford and Bowie go on to show that both the topog raphy of the whole earth and the curvature of the surface must be allowed for, if maximum accuracy of results is to be attained. Thus, at the cost of a truly portentous amount of labor, the theoretical value of gra vity at sea level and at the lati tude of each station was corrected for elevation and the ver tical components of the attractions expected from actual topography and assumed compensation. The result was the computed gravity (gc) at the level of the station. The difference between gc and g, the observed gravity at the sta tion, is called technically the “Hayford isostatic gravity anomaly,” or more simply the “Hayford anomaly.” In either case the name becomes more specific if it is connected with a statement as to the assumed depth of compensation; examples are “Hayford anomaly (113.7 kilometers),” “Hay ford anomaly (96 kilometers),” “Hayford anomaly (60 kilometers).” Gravimetric Test of Isostasy 149 SPECIMEN ISOSTATIC ANOMALIES Table 16 gives a few values of g — gc (rows marked “a”), selected from the list on p. 74 of Report X. These anomalies were computed from Helmert’s spheroid of reference of 1901 (Vienna system). The rows marked “b” give the respective anomalies found during the 1917 investigation (Report XL) when Helmert’s 1901 formula based on Potsdam was used. The rows marked “c” give the anomalies computed in 1934, when the computations were based on the 1930 International spheroid. (See Table 2, on p. 31.)
T able 16 EXAMPLES OF HAYFORD ANOMALIES (depth of compensation 113.7 km). Gals or dynes. (Values a, b, and c according to computations of 1912, 1917, and 1934 respectively)
Theo retical Correc gravity tion for at topog Station Elevation sea level raphy above below the Correc and Computed Observed sea level station tion for compen gravity gravity Anomaly (meters) (To) elevation sation (gc) 00 (S — gc) 1, Key West, Florida (a) i 978.938 0.000 +0.032 978.970 978.969 -0.001 “ (b) u 978.922 (( +0.035 978.957 978.970 +0.013 “ (c) u 978.939 (( +0.035 978.974 978.975 +0.001 43, Pikes Peak, Col orado (a) 4,293 980.079 -1.325 +0.187 978.941 978.953 +0.012 “ (b) (i 980.063 “ << 978.925 978.954 +0.029 “ (c) U 980.078 “ ({ 978.940 978.959 +0.019 81, Sisson, California (a) 1,048 980.298 -0.323 +0.015 979.990 979.971 -0.019 “ (b) (t 980.282 (l (i 979.974 979.972 -0.002 “ (c) (( 980.297 (( U 979.989 979.977 -0.012 COMPARISON WITH THE CORRESPONDING FREE-AIR AND BOUGUER ANOMALIES It will be recalled that the free-air reduction is founded on two inadmissible assumptions: first, that the rock between station and sea level exerts no gravitational attraction; 150 Gravimetric Test of Isostasy meaning, secondly, that there is complete isostatic compen sation for the topography at zero depth (at sea level). On the other hand, the Bouguer reduction, as made by Hayford and Bowie, ignores isostatic compensation “and neglects all curvature of the sea level surface, the topography being treated as if it were standing on a plane of indefinite extent.” (Report X, p. 75.) Table 17 lists a few of the United States stations with
T able 17 COMPARISON OF HAYFORD, BOUGUER, AND FREE-AIR ANOMALIES (depth of compensation assumed at 113.7 km; values a, b, and c according to the computations of 1912, 1917, and 1934 respectively.) Gals or dynes.
Station Hayford Bouguer Free Air (fi “ Sc) (so" — 70) (go — 70) 1, K ey W est, Fla. (a) + 0.006 +0.031 +0.031 “ (b) +0.005 +0.048 +0.048 (c) +0.001 + 0.036 +0.036 43, Pikes Peak, Colo. (a) +0.019 -0 .2 2 1 +0.199 (( (b) +0.021 -0 .2 0 4 +0.216 U (c) + 0.019 -0 .2 1 5 +0.206 81, Sisson, Cal. (a) -0 .0 1 2 -0 .1 2 0 -0 .0 0 4 ff (b) -0 .0 1 0 -0 .1 0 3 +0.013 (( (c) -0 .0 1 2 -0 .1 0 9 +0.003 their Hayford (“new-method”), Bouguer, and free-air anom alies. Here the “1912” anomalies (row marked “a”) were calculated from the Helmert spheroid, modified by subtract ing 7 milligals from Helmert’s value of gravity at sea level of the equator. This modification, giving 978.039 for the constant term of the formula (Vienna system), was made as supplying the reference spheroid which, in 1912, seemed best to fit the observations in the United States. In row “b” will be found the corresponding values reported in Report XL, after the new spheroid just described was itself changed Gravimetric Test of Isostasy 151 by adding 1 milligal to the value of gravity at the Washing ton base station—a correction made for a technical reason. Row “c” gives the respective values when computed by the 1930 International formula. The mean values of 89 anomalies listed in Report X are entered in Table 18.
T able 18 MEAN ANOMALIES FOR 89 STATIONS, FIRST INVESTIGATION (dynes) Hayford Bouguer Free-air anomaly anomaly anomaly Mean with regard to sign - 0.002 -0.065 - 0.001 Mean without regard to sign .018 .073 .028 To Hayford and Bowie, it was clear that the “new method” of reduction furnishes “a much closer approxima tion to the truth than either of the older methods.” (Re port X, p. 77). They inquired whether the new-method anomalies have any systematic relation to the topographic relief. For this purpose the 89 stations were divided into five groups, repre senting as many strongly contrasted topographies surround ing the stations. The conclusion was that the anomalies exhibit no relation to the topography either in sign or average magnitude. This shows that in general the effects of the topography and its compensation have been fully and correctly taken into account in the new method of computation and that the remaining anomalies are due to some cause or causes having no fixed rela tion to topography. (Report X, p. 79.) On the other hand, the Bouguer anomalies show a definite relation to the topography, being in general nega tive and larger the greater the elevation of the station, whereas the new-method anomalies show no relation to the topography; the Bouguer anomalies are four and one-fourth times as large on an average as the new-method anomalies; and if the comparison 152 Gravimetric Test of Isostasy be limited to stations in mountainous regions, the fourth and fifth groups, the Bouguer anomalies are twelve times as large as the ncw-method anomalies (without regard to sign). This is clear and positive proof that the new method of computation is a much closer approximation to the truth than the Bouguer method.” (Report X, p. 80.) In further illustration of the proof, see Figure 32 on p. 162 of the present book. Similar comparison of the three kinds of reduction was made in the case of stations outside the United States, 16 in number. It was found that it is safe to extend the conclusions drawn for the United States to the whole world. The writers are, therefore, confident that if the new method of reduction is applied to a considerable num ber of stations in any part of the world, it will show apparent anomalies which are smaller than those computed by either of the two older methods and thereby show that as a rule, the world over, it is a close approximation to the truth to state that the isostatic compensation is complete and uniformly distributed to a depth of about 114 kilometers. (Report X, p. 83.) Hayford and Bowie discussed at length the maximum errors involved in their work, whether due to faulty obser vation or erroneous computation; the total of the errors was found to be too small to affect in principle the results of their investigation. Less definite conclusions were reached when the effort had been made to evaluate errors due to three basal assumptions: (1) that the isostatic compensation is local to the mathe matical limit; (2) that the depth of compensation is constant at 113.7 kilometers; and (3) that the compensation is every where uniformly distributed to that depth. LOCAL VERSUS REGIONAL COMPENSATION (1) The theory of local compensation postulates that the defect or excess of mass under any topographic feature is uni formly distributed in a column extending from the topographic Gravimetric Test of Isostasy 153 feature to a depth of 113.7 kilometers below sea level. The theory of regional compensation postulates, on the other hand, that the individual topographic features are not compensated for locally, but that compensation does exist for regions of con siderable area considered as a whole. In order to have local compensation there must be a lower effective rigidity in the earth’s crust than under the theory of regional compensation only. In the latter case there must be sufficient rigidity in the earth’s crust to support individual fea tures, such as Pikes Peak, for instance, but not rigidity enough to support the topography covering large areas. Certain computations have been made to ascertain which is the more nearly correct, the assumption of local compensation or the assumption of regional compensation only. In making' such computations it is necessary to adopt limits for the areas within which compensation is to be considered complete. A reconnaissance showed that the distant topography and compen sation need not be considered, for their effect would be practically the same for both kinds of distribution. As a result of this recon naissance it was decided to make the test for three areas, the first extending from the station to the outer limit of zone K (18.8 kilometers), the second from the station to the outer limit of zone M (58.8 kilometers), and the third, to the outer limit of zone 0 (166.7 kilometers). (Report X, p. 98.) It was shown that the American data could not furnish a final, satisfactory test. Nevertheless, Hayford and Bowie believed that the evidence indicates, though it does not prove, that the assump tion of local compensation is nearer the truth than the assump tion of regional compensation only, distributed uniformly to a distance of 166.7 kilometers, or 58.8 kilometers, or even to the small distance 18.8 kilometers from the station. It is also ad mitted as a possibility that an assumption of regional compensa tion only, distributed to some still smaller distance from the station, may be nearer the truth than the assumption of local compensation. (Report X, p. 102.) We shall return to this subject when reviewing Bowie’s later research, in the next chapter. 154 Gravimetric Test of Isostasy RELATION OF ANOMALY TO VARYING DEPTH OF COMPENSATION (2) The second fundamental assumption was given a preliminary test by putting the depth of compensation at 85.3 kilometers and comparing the resulting anomalies with those found when the depth was made 113.7 kilometers. For each depth ten stations gave the same mean anomaly with out regard to sign. The sum of the squares of the anomalies for the smaller depth is 0.003981, while the sum for the greater depth is 0.003529. On the whole, the figures indicate that the depth of compensa tion can not be determined from these ten stations, and probably could not be determined from all of the 89 gravity stations avail able in the United States, with an accuracy nearly as great as that with which it has already been determined from the 765 deflections of the vertical observed in the United States. Hence, it does not seem desirable to make the attempt. . . . It should be noted that . . . a decrease in the assumed depth of compen sation produces a negative change as a rule in the computed effect of topography and compensation and a positive change in the computed anomaly. (3) As it appears . . . that the depth of compensation may be determined from the gravity observations with a low degree of accuracy only, so also it seems evident that there is little hope of determining from the gravity observations the distribution of the compensation with respect to depth. Such an investigation was attempted by the use of observed deflections of the vertical with but little success. (Report X, p. 105.) ANOMALIES IN TERMS OF MASSES What meaning have the new-method anomalies? This important question is complex and will long defy full answer. It can be viewed quantitatively if the arbitrary assumption is made that the whole of each anomaly is due to excess or deficiency of mass under the corresponding station. As an aid to thought, then, Hayford and Bowie prepared the fol lowing table, which gives in dynes the vertical attraction Gravimetric Test of Isostasy 155 produced at a station by a circular mass equivalent to a stratum 100 feet thick; of density 2.67; with radius of 1.280, 166.7, or 1,190 kilometers; and uniformly distributed from the level of the station down to the depths of 1,000 feet, 5,000 feet, 10,000 feet, 15,000 feet, and 113.7 kilometers.
Depth Radius of mass 1,000 5,000 10,000 15,000 113.7 feet feet feet feet kilometers 1,280 meters (outer radius of zone K) 0.0029 0.0018 0.0011 0.0008 0.0000 166.7 kilometers (outer ra dius of zone O) .0037 .0034 .0034 .0034 .0024 1,190 kilometers (outer ra dius of zone 10) .0040 .0037 .0037 .0037 .0035
By change of sign the table is valid also for deficiencies of mass. After illustrating how the table may be used in interpreta tion of actual anomalies, Hayford and Bowie conclude: The preceding considerations show that the typical mean new- method anomaly of 0.017 dyne may be produced by excesses (or deficiencies) of density confined to depths less than 15,000 feet but more than 1,000 feet. But the evidence of the observed deflections of the vertical indicates that probably these typical anomalies are ordinarily produced in part, possibly largely, by excesses (or deficiencies) of density more than 15,000 feet below the earth’s surface, probably as far as 113.7 or 122 kilometersbe- low, for the deflections of the vertical have shown that the iso static compensation if uniformly distributed with respect to depth extends to a depth of 122 kilometers (113.7 kilometers, according to the earlier investigation). Down to this depth there is a relation of subsurface densities to surface elevations. Inasmuch as this relation is apparently maintained with considerable accu racy even when the surface elevations change greatly during the progress of geologic time, there is no apparent changing from time to time of subsurface densities to a depth of 122 kilometers. It is probable, therefore, that the typical anomalies of 0.017 156 Gravimetric Test of Isostasy dyne are produced in part at least by very small excesses (or deficiencies) of density, which extend to as great a depth as the isostatic compensation itself, 122 kilometers, and that the anomalies are produced in part at least by the failure of the processes (whatever they are), which produced isostatic com pensation, to maintain the densities at the precise values neces sary for perfect isostatic compensation. (Report X, p. 110.) As a working hypothesis it was assumed that ordinarily each 0.0030 dyne of anomaly is due to an excess (or deficiency) of mass equivalent to a stratum 100 feet thick. . . . the typical mean anomaly of 0.017 dyne corresponds to a stratum only 570 feet thick. In this typical mean case then the isostatic compensation is so nearly complete that at the depth of compensation (122 kilometers) the pressure is in excess (or less than) the normal for that depth by the pressure due to a weight of a stratum 570 feet thick of density 2.67. This pres sure is only 660 pounds per square inch. A safe working load for good granite used in engineering structures is stated by good authority to be 1,200 pounds per square inch, and its ultimate crushing strength 19,000 pounds per square inch. . . . The new-method anomalies indicate, therefore, that at the depth of compensation the excesses and deficiencies in pressure, referred to the mean value, are upon an average but little more than one-half the safe working load imposed on good granite. . . . These excesses and deficiencies of pressure are a measure of the stress differences at that depth available to produce rup ture. These considerations indicate that the material down to the depth of compensation behaves as if it were considerably weaker than is granite under the conditions existing at the sur face. GENERAL CONCLUSIONS From the evidence given by deflections of the vertical the con clusion has been drawn that in the United States the average departure from complete compensation corresponds to excesses or deficiencies of mass represented by a stratum only 250 feet thick on an average. The gravity determinations indicate this average to be 570 feet instead of 250 feet. In neither case is the average value determined or defined with a high degree of accu Gravimetric Test of Isostasy 157 racy. The difference between the two determinations of the average value, is therefore, of little importance. The determina tion given by the gravity observations is probably the more reliable of the two. Each determination is significant mainly as showing that the isostatic compensation is nearly perfect. (Report X, pp. 111-2.) Other conclusions of Hayford and Bowie may be briefly stated: (1) The gravity anomalies agree well with deflection residuals in delimiting regions in which there are small departures of the density from the mean values corresponding to complete isostatic compensation. Used together in the study of a given region the mutual support given by the two kinds of observations makes the conclusions drawn much more reliable than they otherwise would be. (Report X, p. 121.) (2) The size and sign of the anomalies do not change systematically with the passage from areas of recent, pro longed erosion to areas where there has been recent accumu lation of thick sedimentary rock. (3) There is some evidence that regions of excess of gravity (even after corrections for to pography and compensation have been applied) tend to coincide with high areas on the geoid. . . . The geoid contours can not be used with much success for predicting the sign or amount of the gravity anomalies. The effects on the geoid contours of the excesses and defects of mass below sea level (which produce gravity anomalies) must ordinarily be masked by the greater effects of the topography and its compensation. (Report X, p. 113.) (4) At American stations in pre-Cambrian areas gravity tends to be in excess and at sta tions in Cenozoic areas tends to be in defect. The first case corresponds to excess of mass or undercompensation of topog raphy for all land stations, and the second case to defect of mass or overcompensation of topography for all land stations. . . . 158 Gravimetric Test of Isostasy The excess of mass in pre-Cambrian areas corresponds on an average to a stratum somewhat more than 600 feet thick and the defect of mass in Cenozoic areas to a stratum somewhat less than 400 feet thick. . . . This excess or defect of mass is prob ably distributed through a depth at least as great as 15,000 feet. (Report X, p. 115.) (5) In Switzerland, as in the United States, the isostatic compensation is nearly perfect [and] the isostatic compensation for each feature of the topography lies in general directly beneath that feature, not displaced horizontally. (Re port X, p. 122.) (6) If isostasy is a fact, the Bouguer anomalies should have negative values at inland stations and positive values at sea and on small deep-sea islands. These anomalies should have values increasingly negative as the general ele vation of land increases; and values increasingly positive in oceanic areas as the general depth of water increases. “All these relations between Bouguer anomalies and topography exist.” (Report X, p. 125.) (See Figure 32, p. 162.) In fact, we have here independent proof that isostatic compen sation in a superficial, relatively thin shell of the earth is nearly perfect. (7) In like manner the relation between free-air anom alies and topography imply the reality of close isostatic bal ance throughout the United States. (Report X, p. 125.) 6 LATER GRAVIMETRIC TESTS OF ISOSTASY IN NORTH AMERICA
Rapid increase of field observations by the United States Coast and Geodetic Survey led to the publication of succes sive volumes in the years 1912, 1917, and 1924 (Reports XII, XL, and IC). In all three investigations the isostatic anomalies were calculated with depth of compensation taken at 113.7 kilometers below the earth’s rocky surface, though Bowie ultimately found a depth of 96 kilometers more prob able, if the Hayford-Bowie hypotheses regarding uniformity of compensation in depth and uniform depth of compensa tion be retained. Throughout he assumed the value of gravity at the Washington base station to be 980.112 dynes, the increase of one dyne above the earlier accepted value being caused by a new adjustment of the net of base stations all over the world. The 1917 discussion, as the most com plete, will be summarized in special detail. BOWIE REPORT OF 1912 In Report XII, by W. Bowie, the spheroid proposed by Helmert in 1901 was used as the basis for computing theo retical or “normal” gravity. For 122 stations listed in this volume the resulting mean anomaly was found to be +0.008 ± 0.0014 dyne. Bowie wrote (p. 10): As this mean is five times its own probable error it is believed that it represents a real correction to the Helmert formula . . . 159 160 Later Gravimetric Tests of Isostasy and that this correction should be applied in connection with the new method of reduction for topography and compensation. Accordingly in the following tables the quantities called “Anom aly, New method” are g — (gc + 0.008) in dynes. These are, therefore, the anomalies in gravity as given by the new method and referred to the following formula for the theoretical value of gravity at sea level: To = 978.038 (1 + 0.005302 sin2 - 0.000007 sin2 2). . . . This is equivalent to changing Helmert’s derived value of gravity at the equator but with his flattening retained. . . . A plus sign of the anomaly means that at the station in question the intensity of gravity is in excess of that which would occur there if the isostatic compensation were complete and uniformly distributed to the depth of 113.7 kilometers, while if the anomaly is minus the intensity of gravity is less than it would be if the compensation were complete and uniformly distributed to the depth of 113.7 kilometers. The corrected formula may be called the “Bowie formula No. 1”. It may at once be compared with other formulas, later derived. From the anomalies at 216 United States stations, as computed up to the year 1916 (Report XL), Bowie deduced another formula of reference for the United States, this time taking the depth of compensation at 60 kilometers. The formula is: To = 978.040 (1 + 0.005302 sin2 4> - 0.000007 sin2 2). The corresponding anomalies were distinguished under the name “Hayford 1916.” Also in the 1917 investigation, Bowie derived a reference formula for the world, based on 216 stations in the United States, 42 in Canada, 73 in India, and 17 in Europe—348 stations in all. This “Bowie No.2” formula is: To = 978.039 (1 + 0.005294 sin2 0 - 0.000007 sin2 2). The difference from either of the foregoing formulas is seen to be slight. To permit quick comparison, the formula adopted by the Later Gravimetric Tests of Isostasy 161 International Geodetic Association in 1930 may again be quoted: 7o = 978.049 (1 + 0.0052884 sii2 0 - 0.0000059 sin2 20). BOWIE REPORT OF 1917 Among special features of Report XL the following all deserve mention, even in a comparatively brief summary. (1) Minor corrections were here made in the reduction tables for the effects of topography and compensation in zone C, and some new reduction tables were added for com puting the effects at mountain stations. (2) Sixteen European stations were considered in detail
T able 19 MEAN GRAVITY ANOMALIES IN THE UNITED STATES (gals or dynes) Reference formula for 1912, 1917, and 1924 investigations is To = gm (1 + 0.005302 sin2 0 — 0.000007 sin2 20). Reference formula for the 1934 data is To = gcq (1 + 0.0052884 sin2 0 — 0.0000059 sin2 20). g,t = sea-level gravity at the equator. gw = gravity at Washington base station. Depth of compensation assumed at 113.7 kilometers.
Number Hayford Bouguer Frec-air Data of: of Seq gw anomaly anomaly anomaly stations (g ~ ge) (b'o - 7 0) Uo - To) With regard to sign
1912 (Report X) 87 978.039 980.111 0.000 -0.064 +0.002 1912 (Report XII) 122 978.038 980.112 0.000 -0.048 +0.016 1917 (Report XL) 217 (( << -0.002 -0.036 +0.013 1924 (Report IC) 311 tt tt -0.006 -0.035 +0.009 1934 data 448 978.049 980.118 -0.005 -0.060 +0.003 Without regard to sign 1912 (Report X ).. 0.017 0.072 0.026 1912 (Report XII) .018 .063 .028 1917 (Report XL). .019 .049 .025 1924 (Report IC). .021 .048 .026 1934 data...... 021 .067 .026 162 Later Gravimetric Tests of Isostasy and their data reduced by the Hayford-Bowie method, with depth of compensation at 113.7 kilometers. (3) The isostatic anomalies, computed on the same basis as that used in Report X, were determined for 42 Canadian stations, 73 in India, and 40 in Austria, Germany, Switzer land, Italy, Norway, Bermuda, Saint Helena, Japan, Turkestan, and Alaska. (4) The mean Hayford, Bouguer, and free-air anomalies for 217 United States stations were calculated; the values are given in Table 19. (5) Included in Report XL is a map showing isanomaly
F igu re 32. Contours for Bouguer anomalies in the western United States (milligals). lines for the Bouguer method of reduction. (See Figure 32.) The map indicates that there are decided relations between the Bouguer anomalies and the character of the topography. Therefore it is certain that the earth’s crust is not rigid with oceans and continents held in place as a result of its rigidity. The Bouguer method is cer tainly not based upon correct principles. (Report XL, p. 67.) Later Gravimetric Tests of Isostasy 163 (6) On a second map are drawn the lines of equal free-air anomalies; here a striking relation between these anomalies and the elevations of the stations is demonstrated. (7) A third map bears contour lines for the Hayford 1912, isostatic anomalies. It has not seemed worth while to enter a copy of this map in the present book, but Figure 33 is an analogous showing of the isanomaly curves for the
Figure 33. Positive and negative areas of Hayford 1912 anomalies in the United States. Hayford-Bowie isostatic reduction when all the data up to the year 1934 have been included, the reference spheroid being the International of 1930 and the depth of compensa tion assumed at 113.7 kilometers. Referring to his own map of the Hayford 1912, isostatic anomalies, Bowie wrote (Re port XL, p. 61): The map shows no relation between the anomalies and the topog raphy except for coast topography, but it does show some rela tion between the anomalies and the geological formation. Along the coast, where the geologic formation is generally Cenozoic, the anomaly areas are mostly negative. . . . The presence of light 164 Later Gravimetric Tests of Isostasy material in the earth’s crust near a station would tend to make the computed value of gravity too great and the difference be tween the observed and computed values would tend to be nega tive. [See below.] (8) The Hayford 1916 anomalies give substantially the same evidence in favor of isostasy that is given by the 1912 anomalies, but it is difficult to see which method of reduction is nearer the truth. The mean value for the 1916 anomalies with regard to sign for 217 stations is + 0.001. The mean anomaly for the coast sta tions is — 0.003, which is different from the mean by 0.004. For the 1912 anomalies the mean coast anomaly differs from the mean of all, which is — 0.002. This may be considered as being in favor of a depth of 60 km. as against the depth of 113.7 km. But, as stated above . . . the material near the coast belongs in general to the Cenozoic geologic formation which is less dense than the normal (2.67). The presence of this less dense material makes the computed value of gravity too great and the anomalies negative. The effect of reducing the depth of compensation to 60 km. is to give the compensation of the oceans less effect at the coast stations, the computed gravity is less, and the negative anomalies are reduced in size on an average. It is questionable whether the reduced size of the mean anomaly with regard to sign for the 1916 reduction is evidence in favor of the reduced depth of compensation. (Report XL, p. 68.) (9) There is a decided difference between the mean with regard to sign for the 1912 and 1916 anomalies at stations in mountainous regions above the general level. The former is only -f- 0.001, which shows no systematic error, while the latter is + 0.016, which, on the other hand, shows a great systematic error. The change in depth from 113.7 km. to 60 km. does not make a material difference in the effect of the compensation for the stations in mountainous regions below the general level if there is local compensation of the mountain masses. The table of individual values for the anomalies . . . shows that for this class of topography the anomalies are nearly the same for the 1912 and the 1916 reductions. The table . . . for stations above the general level in moun tainous regions shows that there is little or no similarity between the anomalies by the 1912 and 1916 methods. For the first Later Gravimetric Tests oe Isostasy 165 method there are 9 stations of the 20 with negative anomalies, while for the latter there are only 4. There are only 3 of the 1912 anomalies above 0.030, while there are 6 of the 1916 anom alies. If there is local compensation, then the effect of reducing the depth is to make the effect (negative) of the compensation greater and the computed value of gravity at a mountainous station less. The sign of the anomaly would in consequence tend to be positive. That is what we find to be the case. If the compensation is regional, then the effect of changing the depth of compensation is smaller than if the compensation were local. . . . The conclusion may be drawn that the depth of 113.7 km. is nearer the truth than 60 km. in mountainous regions, and that local distribution of the compensation is more probable than the regional if the latter distribution extends to great distances from the topographic features. (Report XL, p. 69—see the para graph marked “11,” below.) (10) In Report XL, Bowie particularly discussed the
Figure 34. Section showing variation of the horizontal and vertical components of attraction by a unit mass, situated at different depths in the earth (after Barrell). relation of the isostatic anomalies to abnormalities of density 166 Later Gravimetric Tests of Isostasy of the rocks near stations, each of these abnormalities being balanced, deeper down along the same vertical line, by other abnormalities of density with opposite sign. Such balanc ing means isostatic equilibrium, even with a constant depth of compensation, and yet the isostatic anomalies differ from zero, if the masses with abnormal density are of limited horizontal extent. This is apparent as we study the FV curve of Figure 34. Here D is the depth of compensation; the vertical line O — IV is the locus of unit masses corre sponding to difference between normal and abnormal densi ties at the points I to IV, which are located at equal intervals between the (flat) surface and the depth of compensation; R, the horizontal distance between the vertical line de scribed and the station, is arbitrarily made equal to D in length. The curve to the right of the vertical line repre sents the vertical components of the attraction of the unit masses at points O and I to IV; the curve to the left repre sents the corresponding horizontal components. Chiefly by the principle so illustrated, Bowie was inclined to account for the fact that in the United States the Pre- Cambrian and Mesozoic areas (because supposed to be of density above normal) have in general positive anomalies, while the Paleozoic and Cenozoic areas (because supposed to be of density below normal) tend to give negative anom alies. A similar conclusion was reached by White after a later, exhaustive review of the relation between Hayford anomalies and geology in the United States.1 It may be noted at once that, though the relation is clear in many re gions, it can hardly account for the Hayford anomalies in general. Thus, some areas of one-sign anomaly may be explained by irregularities of density in the vertical, isostatic compen sation being complete and essentially local. Other areas of one-sign anomaly may be explained by the existence of re gional compensation, each of these areas being out of com Later Gravimetric Tests of Isostasy 167 plete isostatic adjustment. Barrell described a criterion for distinguishing the two kinds of areas. His instructive discussion will be found in vol. 22 of the “Journal of Geol ogy” (1914, pp. 228-34). He phrased the criterion in the following sentence: A reversal from a large anomaly of one sign to a large anomaly of opposite sign, rather than a small one of opposite sign, marks then in general a passage from an area of excess or deficiency of mass to the opposite. If the masses at I and III, Figure 34, for example, have unlike signs, the sum of their vertical attractions differs from zero, even though the weight of the rock at the vertical line equals that at all distant verticals through the litho sphere. An analogous statement can also be made concern ing the left-hand curve, giving graphically the effect on the horizontal component of the attraction, FH, and therefore on the deflection of the plumb line. See Figure 35, where
Figure 35. Total effect on attraction where unit masses differ in sign and have different depths below the earth’s surface (after Barrell). the continuous curve illustrates the effects when the unit masses at I and III have the same sign, and the dashed line 168 Later Gravimetric Tests of Isostasy illustrates the effects when these masses are of opposite sign. (11) The important question of regional versus local distribution of compensation was considered in chapter VI of Report XL. As a test the anomalies derived on the hy pothesis of perfectly local compensation were compared with the anomalies found after assuming the compensation to be uniform and extending out to the outer limits of zones K, M, and 0—respectively 18.8 kilometers, 58.8 kilometers, and 166.7 kilometers from each of the various stations. The means are given in Table 20.
T able 20 COMPARISON OF ANOMALIES, 122 UNITED STATES STATIONS (gals or dynes)
Local Regional compensation within compensation, distance from station: Hayford 1912 anomaly 18.8 km 58.8 km 166.7 km Mean with regard to sign .000 +.001 + .001 -.001 Mean without regard to sign .018 .018 .018 .019 These values show “that for the country taken as a whole, no one of the methods has an advantage over the others.” (Report XL, p. 87.) When, however, the anomalies at stations in mountainous regions alone are considered, it appeared that regional com pensation to the outer limit of zone O (distance 166.7 kilo meters) is farther from the truth than either regional com pensation to the outer limit of zone M (58.8 kilometers), or than local compensation. (Report XL, p. 91.) (12) The seventh chapter of the Report dealt with the effect of the elevation of a station upon the intensity of gravity. In general this effect, if real, should be most con spicuous when comparison is made between the Hayford anomalies found for two stations which are close together horizontally but with a considerable difference of elevation. Later Gravimetric Tests of Isostasy 169 Three pairs of such stations in the United States, 9 pairs in Europe, and 2 pairs in India were considered, and the essen tial data appear in Table 21.
T able 21 DIFFERENCES OF ELEVATIONS AND ANOMALIES FOR SETS OF NEAR STATIONS Set No. Difference of elevation Difference of anomalic (high-low). Meters. (high-low). Dynes. i ...... 572 ...... +0.004 2 ...... 688 ...... 010 3 ...... 517 ...... 001 4 ...... 1611 ...... 007 5 ...... 531 ...... 012 6 ...... 1,188 ...... 010 7 ...... 1,449 ...... 014 8 ...... 1,138 ...... 013 9 ...... 856 ...... -0.00 1 10 ...... 2,452 ...... +0.028 11 ...... 1,330 ...... 011 12 ...... 896 ...... 033 13 ...... 1,263 ...... 039 14 ...... 1,080 ...... 017 15,571 + .198 It is seen that in only one case is the difference in anomaly negative, and this difference is only 0.001 dyne. On an average a difference in elevation of 100 meters causes a difference in the anomalies of 0.0013 dyne; and a difference of anomaly of 0.0010 dyne is caused by a difference in elevation of 79 meters. (Report XL, p. 94.) Explanation for the algebraic difference in the anomalies, by change in the constant term of the height formula, could be definitely ruled out, and the discussion led to the follow ing statement: We may conclude that the systematic difference in the anomalies at a pair of stations close together, with one high and one low station, is not due to error in the height formula nor to error in the assumed depth of compensation, but that it is due in part to errors in the assumed densities of the topography under the sta tions, to deviations from the normal densities in the material below sea level and in the upper crust, to the use of wide zones 170 Later Gravimetric Tests of Isostasy in computing the effect of the topography, to the probably er roneous assumption that the compensation begins at the surface of the topography, and to the assumption of local distribution of the compensation. That the cause is located in the upper crust rather than in the lower crust is evident from the fact that any deviation from the normal conditions in the lower crust would affect each of the two stations of a pair equally, or nearly so. It is probable that the effect of any one of these causes varies considerably for the different pairs. It would be impossible to arrive at the true effect of each one of the causes for any pair except the effect of the use of the wide zones. The difference in the anomalies is probably due to the combined effect of all of the causes. (Report XL, p. 96.) Barrell discussed the marked correlation of Hayford anomaly and elevation of station and found it to indicate definite error in assuming local compensation. His argu ment is worth quotation as an instructive supplement to Bowie’s statement. Barrell wrote: If a pair of stations be taken close together, one far above the mean elevation, the other far below, they will presumably, because of their juxtaposition, be affected in much the same way by the errors incident to the hypothesis of uniform compensa tion through a depth of 114 km., with complete compensation at that depth. . . . The parts of the anomalies due to the irregu larities and incompleteness of compensation will ordinarily have the same sign and be of nearly the same value at the adjacent stations. This is indicated by the contour lines of Figure 5 [Figure 33 in the present book], which show that in the same region the anomalies are of sufficiently regular gradation in mag nitude to make the drawing of contour lines possible. The parts of the anomalies at the high and low stations due to errors in the hypothesis of local or regional compensation will, however, be of opposite sign. If, then, the algebraic difference of the anomalies for such a pair of stations be computed for successive hypotheses of broader regional compensation, the part of the anomalies due to vertical imperfection of the hypothesis will be largely eliminated. The algebraic difference measures the horizontal imperfection of the hypothesis. That hypothesis is Later Gravimetric Tests of Isostasy 171 favored whose assumed radius of regional compensation gives a minimum value to this algebraic difference. Barrell analyzed the situation at Pikes Peak, Colorado. [His] convincing argument . . . for regional compensation to at least 166.7 km. radius in the vicinity of Pikes Peak is the fact that the algebraic difference of the anomalies between the top and bot tom of the mountain, stations 43 and 42, is less than one-half for regional compensation to 166.7 km. radius than for^the cor responding value given by the hypothesis of local compensation. The decrease in the difference is furthermore progressive with each assumed widening of the zone. The result of adding the more distant stations, 44 and 45, favors regional compensation more markedly but is indeterminate between [zones] M and 0 [radii of 58.8 and 166.7 kilometers]. It would seem, then, that the front range of the Rocky Mountains in Colorado is upheld above the surrounding plains and parks by virtue of the rigidity of the earth.2 Other authorities have seen that the correlation of Hay- ford anomaly with height of station means the rule of re gional compensation. Putnam (see below), Niethammer, Lehner, and Heiskanen may be mentioned.3 Heiskanen has illustrated the argument when the Airy or root type of isostasy is postulated. If such compensation is local, the “crust” under a high mountain peak is thicker than it is under an adjacent valley. If the compensation is broadly regional, the “crust” under the two closely adjacent stations is of nearly uniform thickness (see Figure 8). Hence, with local compensation, gravity at the mountain summit must be greater that it would be with regional com pensation. The anomalies with assumed local compensa tion should, then, be notably positive if the compensation is actually regional. With the valley station the relation would be reversed.* * W. Heiskanen, in “Handbuch der Geophysik,” ed. by B. Gutenberg, Berlin, vol. 1, 1934, p. 917. On p. 894 of this volume, Heiskanen shows how correlation of anomaly with height of station gives a criterion of the best hypothesis of iso static compensation. 172 Later Gravimetric Tests of Isostasy A number of other suitable pairs of stations in the United States and elsewhere are now available, and they tell the same story, though it remains uncertain as to the maximum horizontal spread of compensation for any particular mass of mountains. [ One of the ways in which compensation for topography tends to spread horizontally is illustrated by Figure 36. Divide Consequent Streams | Consequent Streams
INITIAL FORM, IN ISOSTASY ______Sea/eve!
B BEFORE ISOSTATIC ADJUSTMENT ______Sealeve/
Residual "Mountsin’ with Excess Mass
AFTER ISOSTATIC ADJUSTMENT
______t______ISO STATIC t R IS E T______Sealevel F igu re 36. The cause of positive anomaly on a mountain of circumdertudation. Cross section A is that of an arched, smooth belt of land, initially in close isostatic adjustment. The consequent streams running on this constructional topography increase in volume and erosive power downstream from the original divide. Hence the removal of load tends to be more rapid downstream than at the divide, as indicated in section B. If the eroded belt is wide, the lithosphere, finally yielding, is bent upward, and isostatic adjustment is made. A moun tain of circumdenudation with excess of mass is now sur rounded by a belt with moderate deficiency of mass. This stage of pronounced regional compensation is represented in Later Gravimetric Tests of Isostasy 173 section C, where the broken line shows the profile of the initial, arched topography. (13) The effect of changing the depth of compensation on the computed intensity of gravity was systematically tested (chapter VIII of Report XL). Seven different depths were assumed and the anomalies calculated. Table 22 sum marizes the mean anomalies for 218 United States stations, found when equatorial gravity was held at the value in Hel- mert’s 1901 formula, and also when equatorial gravity was changed from that value so as to make each mean anomaly with regard to sign have the value zero. The stations were grouped; each group, occurring in a limited area, gave an average anomaly, which was used in the computation of the mean anomaly for all of the stations.
T able 22 MEAN ANOMALIES VARYING WITH DEPTH OF COMPENSATION AND CHANGE IN ASSUMED EQUATORIAL GRAVITY (218 stations)
Depth of Equatorial gravity: Mean with regard Mean without regard compensation 978.000 gals plus to sign, in milligals to sign, in milligals (kilometers) fraction of a gal: 42.6 .030 + 12 19 << .042 0 16 56.9 .030 + 11 18 <( .041 0 16 85.3 .030 + 9 18 (( .039 0 17 113.7 .030 +6 18 (( .036 0 17 127.9 .030 + 5 18 (t .035 0 17 156.25 .030 +2 18 (( .032 0 18 184.6 .030 -1 19 (( .029 0 19 The summary [Table 22] alone gives no strong evidence in favor of any one depth of compensation, for the means without regard to sign have little change from one depth to another while the mean with regard to sign is made the same (zero) for each depth. (Report XL, p. 107.) 174 Later Gravimetric Tests of Isostasy The most probable depth was determined by a graphic method. In a general review of the subject, Bowie wrote: The group of publications of the Coast and Geodetic Survey deal ing with deflections and gravity values shows that isostasy exists in a form nearly perfect in the United States as a whole, also that there is nearly perfect isostasy in areas which form comparatively small percentages of the area of the entire country. The conclusions which may be drawn from the investigation reported in this volume substantiate to a great extent the con clusions arrived at from previous investigations. This is an important fact, for 70 per cent more gravity stations in the United States were used at this time than in the preceding grav ity investigation and many stations in Canada, India, and Europe, for which data were available, were also used. The depth of compensation was derived from the 216 stations in the United States and was found to be 60 km. When the sta tions were divided into different groups, other depths were ob tained. They agreed in general with the value determined from all of the stations. An exception is in the case of the stations in mountainous regions, 56 in all. The values of the depth of compensation determined from these are 111 km. and 95 km. on two somewhat different assumptions. Owing to the fact that at stations in mountainous regions above the general level the values of gravity are very sensitive to a change in depth, it is believed that the value of the depth determined from the sta tions in mountainous regions has greater strength than the other values. The author believes that the best value for the depth of com pensation is the mean of the Hayford value of 97 km., which was obtained from deflection data at stations in mountainous regions and the value of 95 km. derived from gravity data in mountain ous regions. This mean is 96 km. The author believes that future values of the depth of compensation derived from much more extensive data will fall between 80 and 130 km. (Report XL, p. 133.) BOWIE REPORT OF 1924 Seven years after the appearance of Special Publication No. 40, the United States Coast and Geodetic Survey pub Later Gravimetric Tests oe Isostasy 175 lished Special Publication No. 99 on “Isostatic Investiga tions and Data for Gravity Stations in the United States Established since 1915,” also by William Bowie. This re port, “IC,” is in two parts—one part giving observed and calculated values of gravity at each of 85 new stations; the other part summarizing Bowie’s ideas on isostasy and re lated subjects after studying the additional data. Some of his conclusions are to be quoted, for they facilitate review of the complex subject. When the proper corrections are made in accord with the hypothesis of isostasy, the anomalies in the geodetic data are reduced from one-seventh to one-tenth of what they would be if there were no such irregularities as the theory of isostasy postulates. The small anomalies which now remain may be due to lack of uni formity in the distribution of the abnormal density and to devia tion from uniform pressure on the imaginary surface [depth of compensation], but probably they are mostly due to very abnor mal densities of materials close to the geodetic stations. The significant facts relating to isostasy are: The sea-level sur face of the earth is very nearly a spheroid; the distribution of density with depth is about the same along all radii of the earth; the irregularities in the direction of the plumb line and in gravity values are due to causes near the earth’s surface; and these irregu larities are largely due to the uneven surface of the earth and deviations from normal densities in the earth’s materials extend ing to a distance of the order of magnitude of 100 kilometers (about 60 miles) below sea level. Concerning the relation of geoid to spheroid of reference, we read: In the investigations reported on in The Figure of the Earth and Isostasy, it was shown that the total range of the geoid surface below and above the spheroid for those portions of the United States considered is 37.75 meters, about 124 feet. It may be assumed that for this area the actual maximum deviation of the geoid from the spheroid is only one-half this amount or 19 meters (about 62 feet). 176 Later Gravimetric Tests of Isostasy The area of the United States is about 3,000,000 square miles and that of the globe is about 197,000,000 square miles. It would not be justified to predict that no greater deviation of the geoid and spheroid surfaces will be found in other areas, yet what is found in the United States is a good indication of what may exist elsewhere. It is probable that the geoid is above the spheroid by as much as 100 meters under great mountain masses like the Himalayas and the Andes. . . . The effect of a mountain mass in tilting the geoid is greatly lessened by the isostatic equilibrium of the earth’s crust. As blocks of the earth’s crust of equal cross section have very nearly the same mass, the density of the material of a block under a mountain mass will be less than normal. The deficiency of mat ter under a mountain mass tends to nullify the effect of the moun tain mass on the tilt of the geoid surface. Close to the mountain the mountain’s effect greatly predominates, but at a distance of about 140 miles the effect of the isostatic compensation (defi ciency of matter under the mountain) will almost offset that of the mountain. At this distance the effect of the mountain is reduced 90 per cent. This is a very important point, and it makes necessary a revision of some old estimates of the extent to which continents, with their high land, tilt up the geoid surface. It has been held that the geoid must be much below the spheroid out in the oceans, but this is probably not true. At a short distance from the coast the effect of the land masses will be offset by the isostatic compensation, and only the irregular configuration of the bottom will vary the relative positions of the geoid and spheroid surfaces. The effect of the continental shelf may be large, but, as in the case of land masses above sea level, it will be offset by the defi ciency of density in the material of the block under the shelf, as compared with the density of the material of the crust under the deeper water. From a consideration of all the evidence, we may conclude that the deviation of the geoid from the spheroid is probably not more than 100 meters over a great ocean “deep,” and that the area affected by such deviation is quite limited in extent. Over land areas the deviation may be as much as 100 meters under some of the great mountain systems. It will be seen that, as compared with the smooth mathematical surface of the spheroid (the mean surface), the geoid has bumps and hollows of moderate sizes. Later Gravimetric Tests of Isostasy 177 If there were no isostatic equilibrium in the earth’s crust, the bumps and hollows on the geoid might be from 30 to 40 times greater. Considering the insignificant size of the deviations of the geoid from the spheroid we can readily understand that such deviations are not factors in dynamic and structural geology. . . . The only way to derive from triangulation and astronomic observations the mathematical surface or spheroid for the whole geoid would be to have connected triangulation over all the earth. This is not possible, because the great land areas are separated by large bodies of water across which geodetic measurements can not be made. It is very probable that the process of elimi nating the local deviations of the geoid caused by the attraction of the topography and compensation for the area of the United States has enabled us to obtain a spheroid which represents the mean surface of the earth very much closer than if we attempted to compute the mean spheroid from the actual uncorrected geoidal surface. . . . It is believed that, if the isostatic method were applied in the computation of the spheroid in each of a number of large sepa rated areas, the derived spheroids would have a very close agree ment. It seems equally certain that they would differ consider ably if derived by the older methods [Bouguer and Free Air reduc tions]. (Quotations from pp. 4-8, Report IC.) After expressing doubt that Helmert was justified in put ting a longitudinal term in the formula for the earth’s figure (1915 formula), Bowie wrote: The complete gravity formula really should be of the form go = g (1 + Ci sin2 4> — C2 sin2 2
UNITED STATES VALUES OF GRAVITY REPORTED SINCE 1924 The Coast and Geodetic Survey has occupied many hun dreds of new stations in addition to those described in the quarto volumes issued between 1910 and 1924. The results of the observations and reductions have been distributed in the form of mimeographed tables entitled “Principal Facts for Gravity Stations in the United States.” The first was sent out in 1934, giving data for all stations, new and old, and 457 in number. Similar tables, published as Parts 2, 3, 4, and 5 of the series, give respectively the data for stations 458 to 586, 587 to 713, 714 to 925, and 926 to 1081; Part 5 was issued in 1940. All reductions for the five Parts were Later Gravimetric Tests of Isostasy 183 based on the 1930 International formula for the earth’s figure, and on the (1933) value of gravity, 980.118 dynes, assumed for the new base station at Washington. In order to see how far the additional facts might modify conclusions drawn from the facts available in 1924, the mean anomalies for 448 stations, reported in Part 1 (1934) have been computed and entered in Table 19. Small differences from the results won at 311 stations of the 1924 record were disclosed, but these differences are in large part explained by the influence of concentration of many of the new stations in three quite limited areas of Alabama, Texas, and Wyoming. There measurements of gravity were multiplied for special reasons, and the results given in Table 19 represent some overweighting for such regions, when means for the country as a whole were calculated. Concentration of stations in limited areas is even more evident in the tables of Parts 2, 3, and 4, and there is need of proper weighting before useful means can be derived from the full data of 1938. Part 4 contains a list of 242 isostatic, Hayford anomalies, previously reported but now embodying a new correction for topography, zones A to O, a correction based on Bullard’s modification of the Hayford mode of measuring the effect. See p. 136. Parts 4 and 5, describing the data for stations 714 to 1081, also introduce for the first time values of the “indirect” isostatic anomaly, that is, the anomaly found when the theo retical gravity at the station is calculated from the position of the reference spheroid at the vertical through the station, rather than from the corresponding point on the geoid (ordi nary Hayford anomaly). See p. 126. With depth of compensation in each case taken at 96 kilometers, the maxi mum difference between the two kinds of anomaly through out the whole series of 212 stations here reported is 5 milli- gals. In average the difference is only 3 milligals—hence of no great significance in the problems of this book. 184 Later Gravimetric Tests of Isostasy PUTNAM’S DISCUSSION OF UNITED STATES DATA As far back as 1895, G. R. Putnam had occupied 25 gravity stations between the Atlantic coast of the United States and high points in the Rocky Mountains. He reduced the ob served values of gravity by his “average-elevation method” (average compensation distributed out to a distance of 100 miles from each station). This method was in effect based on the assumption that the compensation for topography is regional instead of purely local. After the appearance of Bowie’s Report XL, Putnam repeatedly emphasized the computational errors involved when the isostatic compensa tion for topography is assumed to be quite local. From one of his papers, already noted in chapter 4, we further read: There is good evidence that the departures from complete local compensation are sufficient in their effect as shown in anomalies of gravity to require that they be considered in a complete and systematic reduction of gravity observations. [The evidence] is based on the fact that in a regional, as compared with a local distribution of compensation, the amount of compensation beneath the zones in the vicinity of the station will be less for stations above the general level, and will be more for stations below the general level; and the anomalies for the “above” sta tions will be smaller algebraically, and for the “below” stations will be larger, than the local compensation anomalies; there may be an opposite effect in remoter zones, but this, on account of the greater distance, will only partially offset the effect in the near zones. This evidence is summarized under three heads, a, b, and c. (a) Comparison of the anomalies of pairs of stations close to each other horizontally, but of considerable difference of eleva tion, has the advantage of largely eliminating distant effects and other sources of error. Results are available for 16 such pairs, with height differences from 531 to 2,452 meters. With one minor exception, these show in every case a positive difference when the Hayford anomaly for the lower station is subtracted from that of the higher, the average difference being + 0.015 Later Gravimetric Tests or Isostasy 185 dyne. This difference is of the sign to be expected from an error due to using complete local compensation, and is evidence of its existence. It is of a size appreciable in gravity reductions, being about the size of the average gravity anomaly. If the difference is due to this cause, and assuming, as is indicated, that it is related to the difference in elevation, it corresponds to an average error in high mountainous regions of + 0.0014 dyne for each 100 meters greater elevation. (b) For stations in mountainous regions, the Hayford anom alies have been grouped for stations above and for stations below the general elevation within 100 miles, in the order of the dif ferences from the general level, and for these stations there have been computed also the anomalies with compensation based on the assumption that the surface about each station is leveled off to a radius of 37 miles from the station, this area being desig nated by zone M, and this has also been done for a radius of 104 miles, designated as zone O. These latter represent an approxi mate application of regional compensation, but for distinction they are here designated as “average level anomalies.” Compar ing the zone M or the zone O anomalies with the Hayford local anomalies, it is found that in nearly all cases the local anomaly is algebraically larger when the station is above the general level, approximately in proportion to the elevation difference, and is smaller in similar proportion when the station is below the gen eral level. . . . As the local anomaly should be the larger for “above” stations, and the smaller for “below” stations, it is rea sonable to ascribe these systematic differences also to error due to a reduction based on complete local compensation. . . . The factor of 0.0014 dyne for each 100 meters above the gen eral level, found under (a), is derived from pairs of stations in very mountainous regions, often with one of the stations near a high summit. Consideration of the distribution of the load of high mountains makes it reasonable to assume that this factor varies in some relation to the height above the general level, or in other words that the difference between the local anomalies and the correct regional anomalies increases by some function of the elevation difference greater than a simple proportion. Inspec tion of the anomalies indicates this to be true. For the present examination of this subject it is considered sufficient to use the factor 0.0014 dyne per 100 meters for stations from 1,000 to 2,500 meters above the general level, and to halve this factor for 186 Later Gravimetric Tests of Isostasy stations of smaller difference of elevation, and to double it for the one station which is of much greater difference of elevation. The corrections to the Hayford anomalies on account of local compensation . . . are positive for stations below the general level, and negative for stations above. The corrected anomalies thus obtained are designated “regional anomalies”. . . . All of this is therefore substantial evidence against complete local compensation. (c) For five of the pairs of adjacent stations previously referred to there are available comparative anomalies from com putations on the basis of complete local compensation, and of average level compensation to three different zones, and table B shows the pair differences of these comparative anomalies, arranged in order of difference of elevation; also in column 5 the regional anomaly differences are shown as derived by applying corrections to the Hayford local anomalies in the manner just described. . . . The results for the mountain pairs systematically favor regional compensation, or average level compensation, as com pared with local compensation.4 In the same paper, Putnam inserted a diagram to illus trate the three kinds of compensation described; this dia gram is reproduced as Figure 25 (p. 124). He also outlined “a plan for the practical application of limited regional com pensation in the reduction of gravity observations”—the “regional isostatic reduction.” In a later communication, Putnam made relevant notes: From the nature of the case, the evidence as to depth of com pensation depends principally on results in mountainous regions. But it is just in these regions that the errors resulting from the assumption of local compensation become significant. It is therefore evident that depths of compensation thus derived will differ from depths computed on a correct hypothesis of some degree of regional isostasy. The overcompensation of summit stations will be reflected by too large a depth of compensation. This effect is shown in the varying results for the depth, derived from stations grouped according to topographic location. A simpler assumption for study of this problem of vertical distribution would be that of an “effective depth of compensa Later Gravimetric Tests of Isostasy 187 tion”, at which the whole compensation should be considered as concentrated; this would be a frankly imaginary conception, and as such would avoid apparent conflict with the realities of nature. This idea will be followed in this paper. . . . The earlier publications of the Hayford reduction results gave a maximum regional effect as a zone of about 12 miles radius, or an area of about 500 square miles. This is less than one-sixtieth part of the block of over 30,000 square miles, now indicated as possibly having some regional compensation; the Hayford anom alies are actually computed on the basis of completely compen sated blocks or columns having a surface area so small that 200,000 such blocks equal 1 square mile.5 GILBERT’S ESTIMATES OF UNCOMPENSATED LOADS In 1895, Gilbert discussed Putnam’s observations and con cluded that the “plateaus” of the United States, ranging from 100 to 8,700 feet in height, are approximately in iso static equilibrium. Basing his own calculations on the Clarke spheroid of 1880, Gilbert found the great central plain of the United States to be so nearly balanced that the departures from equilibrium represent positive or negative loads no greater than the weight of about 240 feet or 73 meters of rock. Considerably greater departures were com puted for the Rocky Mountains and the Yellowstone Na tional Park.8 HEISKANEN ON GRAVITY IN THE UNITED STATES In 1924, W. Heiskanen of the Geodetic Institute of Fin land published the first of his extraordinarily significant pa pers dealing with the gravimetric test of isostasy.7 Here, for the first time, the anomalies based on the Airy hypothesis were compared, systematically and on a large scale, with the anomalies based on the Pratt-Hayford hypothesis. In this discussion observations in Europe as well as in the United States were used; hence this paper will be noticed in the next chapter. A second study of isostasy in the United States, consid 188 Later Gravimetric Tests of Isostasy ered alone, was described three years later.8 With clear sanction from geology and seismology, Heish ■ en saw reason to adopt Airy’s "root” idea but objected to the postulate of uniform density for the sial or Airy’s “crust of the earth.” Heiskanen’s suggestion of a better distribution of densities was noted in chapter 4 of this book. To the details there described he added the premise that the “crust” under the Atlantic is 25 kilometers thick (following Gutenberg in his estimate, derived from seismological data), and of density 2.83, the “crust” under the Pacific (made of sediments) be ing 0-5 kilometers thick and with density of 2.40. For Heiskanen’s modification of the Airy scheme of densities see Figure 24, p. 123 of this book. All anomalies calculated refer to the Helmert 1901 formula (Potsdam system); see Table 2, p. 31. With similar assumptions made, a fuller discussion was published in 1932.9 The more important results will be abstracted. The purpose was to test four different explanations of isos tasy by comparing their respective anomalies at 313 sta tions in the United States. These hypotheses are: (1) Hayford’s: Local, complete, uniform compen sation to depth of 113.7 kilometers; (2) Heiskanen’s: The Airy hypothesis modified by assuming vertical increase of density in sial and sima, the sea-level thickness of the sial being taken at 50 kilo meters; (3) Airy’s: Uniform density for the sial, assumed to have a sea-level thickness of 40 kilometers; uniform density for the sima; (4) Airy’s: Like (3) but assuming a sea-level thick ness of the sial or “crust” at 60 kilometers. With regard to sign, the mean anomalies of all 313 stations came out as follows: (1) Hayford...... + 6 milligals (2) Heiskanen...... -J- 9 milligals Later Gravimetric Tests of Isostasy 189 (3) Airy (40 kilometers)...... + 9 milligals (4) Airy (60 kilometers)...... +5 milligals For the purpose of comparison, these means were sub tracted respectively from the individual anomalies that had been derived from the Helmert 1901 formula. The means of the final values were instructively arranged in groups, as shown in Table 24.*
T able 24 MEAN ANOMALIES WITH REGARD TO SIGN, BY GROUPS (milligals; Helmert 1901 formula)
Hayford Heiskanen Airy Airy (40 km) (60 km) Group I: 23 stations on Pacific coast -23 -18 -20 -2 4 “ II: 25 stations near Pacific coast -23 -19 -20 -23 " III: 37 stations in mountains, below the general level 0 0 + 1 0 “ IV: 24 stations in mountains, above the general level +9 +8 +8 + 1 “ V: 32 stations on Atlantic coast - 6 - 4 -3 -5 “ VI: 55 stations near Atlantic coast -2 -1 0 0 “ VII: 100 stations in flat land + 1 0 0 + 2 Variation of the means for the groups 31 27 28 26 Their variation, groups I and II excluded 15 12 11 7
The mean anomaly in a broad belt along the Pacific shore is strongly negative. Heiskanen finds explanation either in local abnormalities of rock density, or by assuming that the sial is here thinner than in the United States generally, or by assuming both influences at work. The mean anomaly for the 32 stations at the Atlantic coast (group V) is more mildly negative, under all four hypotheses. Comparison of the four sets of mean anomalies is specially telling in the cases of groups III and IV. The second Airy hypothesis (60 kilometers) gives nearly the same mean * If the International formula be used as basis of reduction, all values would be about 14 milligals more negative. 190 Later Gravimetric Tests of Isostasy anomaly for both groups, while the other three pairs of values show respective differences of 9, 8, and 7 milligals. These facts favor the second Airy hypothesis. Each of the four methods of reduction shows the mean anomaly at the 61 mountain stations to increase with station height. This tendency is least conspicuous with the second Airy hypothesis, which therefore again ap pears to be nearer the truth than any of the others. The correspondence of the Airy hypothesis would be still closer if the mountains be assumed to have a root with maximum lower limit below the 60-kilometer level. However, the dependence of the anomalies on station height probably means that the compensation of the mountains is not local but regional. If, finally, a criterion for the best hypothesis is found in minimum variation of the group means, the Heiskanen and two Airy schemes of density are to be preferred to Hayford’s, and the second Airy hypothesis (60 kilometers) is slightly better than any of the other three. Thus, three tests—the average deviation of the individual anomalies from the group means, the degree of dependence of the anomalies on station height, and the variation of the group means—appear to favor the two Airy and Heiskanen hypotheses rather than the Pratt-Hayford. In this statis tical study no clear choice was indicated between the better Airy hypothesis and that of Heiskanen, but, on the other hand, the latter has an advantage in being founded on in formation from seismology, while both the Airy idea and the Pratt-Hayford idea are “pure working hypotheses.”10 GRAVITY IN CANADA For many reasons, it is gratifying to know that the Cana dian Department of the Interior has begun the measurement and reduction of gravity values over the Dominion, an area larger than that of the United States proper. A valuable Later Gravimetric Tests of Isostasy 191 record of results available at the beginning of the year 1936 is the memoir by Miller and Hughson published during that year at Ottawa.11 The volume contains a map showing the areas of one-sign anomaly (Hayford-isostatic, 113.7 kilometers) for the whole of the United States proper and a broad belt of southern Canada, this comprising nearly one fourth of the Dominion. The map clearly indicates the northward continuation of the wide belt of negative anomaly that stretches along the Pacific coast from Mexico to the boundary between Washington State and British Columbia. Between 49° and 56° of North Latitude and between 118° and 130° of West Longi tude the mean anomaly is about —11 milligals, the mean for the United States part of the belt being about —16 milligals. The analogous negative belt along the Atlantic coast of the United States is seen to be continued throughout the 500-kilometer length of Nova Scotia and Cape Breton Island, where the mean anomaly is approximately —8 milligals. Another outstanding feature of the investigation is em bodied in Table 25, which gives for the 126 Canadian stations the mean anomalies when the Airy and Hay ford hypotheses, with various depths of compensation, are applied. In the former case, the difference of densities for the sial (“crust”) and sima (“substratum”) is assumed to be 0.6; as Heiskanen has shown, the results would not be decidedly changed if this difference had been taken at 0.3. (See p. 122.) So far as they go, the data seem to show that the sea-level thickness of the sial (Airy hypothesis) is close to 35 kilo meters ; and the depth of compensation (Hayford hypothesis) is close to 85 kilometers. CONCLUDING REMARKS The facts recorded in this and the fourth and fifth chapters show that isostasy governs in North America. The proof 192 Later Gravimetric Tests of Isostasy has come from two independent tests in the field—tests with plumb line and with gravity pendulum. Measurement of
T able 25 MEAN ANOMALIES, 126 CANADIAN STATIONS (milligals; Internationa] formula)
Mean with Mean without Sum of squares of regard to sign regard to sign anomalies in units of 1O"0 Airy hypothesis—thickness of sial (km): 15 +4 15 41,617 20 +4 15 39,273 30 +3 14 37,177 40 +2 14 37,191 60 0 14 40,570 80 - 3 15 45,727 Hayford hypothesis—depth of compensation (km); 42.6 + 1 14 41,185 56.9 + 1 14 39,364 85.3 0 14 38,224 113.7 -2 14 39,191 127.9 - 2 14 40,149 156.25 -3 15 42,850 Free-air reduction -1 4 25 146,360 Bouguer reduction -57 59 353,981 the intensity of gravity itself furnishes a double test, founded on the ranges of both Bouguer and isostatic anomalies. The exact mode of compensation for the topography of the continent is not apparent, though the Airy hypothesis, assuming the compensation to be uniformly distributed in sialic roots at moderate depths, seems slightly preferable to the Pratt-Hayford hypothesis of uniform compensation to uniform depth. That the southern Sierra Nevada has a root, whose reality can be established by seismological evi dence, is a conclusion from a recent study by P. Byerly. He was able to show that this root extends at least six kilometers below the normal level of the bottom of the sial under California.12 Tests of all the hypotheses lead to the conclusion that the Later Gravimetric Tests of Isostasy 193 center of gravity of compensation is somewhere between 40 and 50 kilometers below sea level. A tailing-out compensa tion to a depth much greater than 50 kilometers is not ex cluded; that is, there is no direct evidence that the astheno- sphere is perfectly weak. All investigators, including Hayford and Bowie, have ap preciated the fact that perfectly local compensation for topography is a fiction, adopted for mathematical conven ience and manifestly representing an unreal condition. Explicit proof of regionality of the compensation was early presented by Putnam and others, when they noted the rela tion of the sizes of the isostatic anomalies to the elevations of the respective stations above sea level. After reductions are made according to the Pratt-Hayford, Airy, Heiskanen, and Putnam modes of compensation, and the corresponding anomalies are plotted on a map, the conti nent is seen to be divided into alternating areas of positive and negative anomaly (for example, see Figure 33). What ever hypothesis of compensation is adopted, the widths of the broader areas of one-sign anomaly remain of the same order, and the sign of the anomaly is unchanged. It is a fact, however, that the spans of the areas of one-sign anom aly tend to decrease as the network of gravity stations is in creased. Correspondingly, the amplitudes of the “waves” of anomaly tend to diminish. See p. 356. It further appears that a few areas of one-sign anomaly will be conspicuous even after an indefinite increase in the number of stations evenly distributed over the continent. This is particularly true of the broad negative belt along the Pacific coast and is probably true of the narrower nega tive belt along the Atlantic coast. The former represents the greatest irreducible field of anomaly in the United States. Its large dimensions mean a particularly serious challenge for the theory of ideal isostasy—that is, isostasy defined in terms of thin lithosphere and infinitely weak asthenosphere. 194 Later Gravimetric Tests of Isostasy How the challenge can be met is a speculative question, to be discussed in chapter 12. It also looks as if the glaciated tract of the northeastern United States and eastern Canada is another area of irreducible negative anomaly. We note, finally, that in a general way the actually mapped areas of one-sign anomaly agree in position with the expected humps and hollows of the geoid, as determined by plumb-line studies. However, this corroborative test of isostasy and its localized failures is limited, because the tri angulation net giving the geoidal data is restricted to narrow belts which together cover only one or two per cent of the continent. The reality of uncompensated loads on the North Amer ican sector of the globe is clearly important for our main problem—that concerning the distribution of terrestrial strength. The discussion of that relation is postponed while we gather additional facts bearing on the subject. In turn we shall look at results of studies of gravity in Europe, Africa, and Asia, over the oceans, and in the glaciated tracts.
R e fer en c es 1. D. White, Bull. Geol. Soc. America, vol. 35, 1924, p. 207. 2. J. Barrell, Jour. Geology, vol. 22, 1914, p. 161. 3. G. R. Putnam, U. S. Coast and Geodetic Survey Report, App. 1, 1894; Proc. Nat. Acad. Sciences, vol. 14, 1928, p. 407; Jour. Geology, vol. 38, 1930, p. 590; T. Niethammer, Verhand. Schweiz. Geodat. Kommission, 1921; M. Lehner, Verhand. Schweiz. Naturj. Gesell., 1930; W. Heiskanen, Verojfent. Finnischen Geodat. Inst., No. 6, 1926. 4. G. R. Putnam, Proc. Nat. Acad. Sciences, vol. 14, 1928, pp. 407-12. 5. G. R. Putnam, Jour. Geology, vol. 38, 1930, pp. 593 and 596. See G. R. Putnam, Report U. S. Coast and Geodetic Survey, 1894, App. 1; Amer. Jour. Science, vol. 1, 1896, p. 186; Bull. Geol. Soc. America, vol. 33, 1922, p. 287. 6. G. K. Gilbert, Jour. Geology, vol. 3, 1895, p. 331. Later Gravimetric Tests of Isostasy 195 7. W. Heiskanen, Pub. No. 4 of the Geodetic Institute of Fin land, 1924. 8. W. Heiskanen, Zeit.f. Geophysik, vol. 2, 1927, p. 217. 9. W. Heiskanen, Annales Acad. Sci. Fennicae, vol. 36, No. 3, 1932. 10. W. Heiskanen, op. cit., p. 133. 11. A. H. Miller and W. G. Hughson, “Gravity and Isostasy in Canada” (Pub. of the Dominion Observatory, Ottawa, vol. 11, No. 3), 1936. 12. P. Bycrly, Bull. Seism. Soc. America, vol. 29, 1939, p. 462. 7 TESTING ISOSTASY IN EUROPE
INTRODUCTION The European literature on gravity in its relation to the earth’s figure is extensive; here we shall confine attention to the more significant researches bearing on isostasy in Europe. The review may well begin with a word about F. R. Hel- mert’s monumental “Hohere Geoddsie” (Leipzig, 1884), an exhaustive study of the science on which our reasoning is naturally based. Helmert co-operated in planning the field campaign of R. von Sterneck, who from 1890 to 1895 used the reversible pendulum of his own design to measure gravity at hundreds of stations distributed over central Europe.* A rapid accumulation of field data enabled Helmert, in 1901, to publish an improved formula for the mathematical figure of the earth. We recall that this spheroid of reference was used during the path-breaking investigations of Hayford, Bowie, and Heiskanen, though each of these workers saw. need for still further bettering of the formula. Even so, Helmert’s formula (founded on the Potsdam system) is still important, for the reason that the much-used compilation of gravity values all over the world, the tables of Borrass, are phrased in terms of the formula.1 Until recently European geodesists and geologists have devoted special attention to Bouguer and free-air anomalies, * See R. von Sterneck, Mill. kon. und kais. Militargeograph. Inst., Vienna, 1892, 1894 Note should also be taken of Helmert’s classic paper on “Die Schwer- kraft und die Massenverteilung der Erde” (Encye. math. Wiss., vol. 6, Heft 1, Leipzig, 1910). 196 Testing Isostasy in Europe 197 and for the most part have refused to follow the lead of Put nam and Hayford in emphasizing the isostatic anomalies. One of the first systematic attempts to find how mountain relief is supported by compensating defect of density under that relief was made in 1907 by Costanzi, who, like von Ster- neck before him, published a Bouguer isanomaly map of Central Europe.2 During the same year Deecke discussed the Bouguer anomalies for the western Mediterranean re gion, including the Apennines.3 He explained areas of ex cess density, such as the Adriatic, as due largely to localized compression of the lithosphere; and the deficiency of density in other areas by assuming looseness of texture of the corre sponding rocks, whether this looseness be due to the sedi mentary origin of the rocks or to orogenic brecciation. These theoretical suggestions as inclusive explanations are clearly without adequate support.4 GRAVITY IN ALPS AND APENNINES The geodetic commission of the Schweizerische Naturfor- schenden Gesellschaft has covered an exceptionally dense net work of gravity stations within the homeland. The data regarding free-air, Bouguer, and isostatic anomalies, sup plied by F. Niethammer and M. Lehner for 231 stations, have been tabulated in Heiskanen’s world Catalogue.6 From that list the means of the anomalies, computed by the
T able 26 MEAN ISOSTATIC ANOMALIES FOR SWITZERLAND, WITH REGIONAL COMPENSATION (milligals; 231 stations with average elevation of 967 meters)
Assumed value Area (A) without Mean isostatic Mean free-air Mean Bouguer of T (km) compensation anomaly anomaly anomaly (km square) 100 8 X 8 -5.7 -10.6 -115 100 64 X 64 -6.9 ------■------100 128 X 128 -11.6 — — 80 64 X 64 +0.4 — — 198 Testing Isostasy in Europe 1930 International formula and according to four different assumptions, have been calculated and entered in Table 26. There T represents the depth of Hayford compensation, and A represents the rectangular area centered at each station and assumed to include topography which is not isostatically compensated. The table tends to show that in Switzerland the compen sation for topography is, as expected on mechanical grounds, regional; and that the center of gravity of the compensation is, in average, not far from the depth of 40 kilometers below the mean surface of the country. At intervals between 1915 and 1921, Albrecht Heim pub lished his views about the geological meaning of the Swiss field of gravity. He found himself in whole-hearted agree ment with the root (Airy), isostatic explanation of the Al pine relief, and also with the theory of nappes. In free translation, we read: The fold-complex of the Alps, extending deeply into the earth’s crust, is floating much as icebergs float in the sea, and this condi tion has been reached, not because of dislocations in the horizon tal sense but primarily because of the sinking of the superposed nappes, after this pile has been thickened through horizontal compression of the region.6 Heim estimated the extra thickness of the sial to be 20 to 25 kilometers in maximum; by so much the root extends down ward, below the normally placed bottom of the sial.* In 1920, Kossmat made an outstanding contribution. He thought that the mapping of isanomalies computed on the Hayford premises could not lead to results useful to the geol ogist, and he dwelt particularly on the significance of the * Other references to Heim’s writings are: Vierleljahrschrift Naturf. Gesell., Zurich, vol. 61, 1916, p. 93; Jakrb. Schweiz. Alpenclub, vol. 53, 1919. E. A. Ansel (“Handb. der Geophysik,” ed. by B. Gutenberg, Berlin, vol. 1, 1934, p. 541) states that from seismological evidence Gutenberg showed the “granitic” layer of the sial under the Alpine axis to be 30 to 35 kilometers in thickness, while in northern Germany the layer does not exceed 10 kilometers in thickness. T esting Isostasy in Europe 199 Bouguer anomalies.7 The distribution of these in Central Europe was indicated on a colored map, later reproduced in black and white by Born, and again in Figure 37 of the pres-
Figure 37. Bouguer anomalies (milligals) in central Europe (after A. Born; courtesy of Julius Springer, Berlin). 200 Testing Isostasy in Europe ent book. The map gives the anomalies of mass below the geoid of that part of the continent. Figure 38 gives a cross-profile of the mountain system,
F ig u re 38. Bouguer anomalies in section across the Alps (after Kossmat). from Juras to Apennines, along a northwest-southeast line passing through Lake Geneva, the Chablais Alps, Monte Rosa, and the environs of Turin.8 A few thrust-planes and other structural elements are diagrammatically represented. The broken line below indicates the varying Bouguer anom aly, in terms of the attraction of an extensive plate of rock with density of 2.4. The maximum anomaly corresponds to the attraction of such a plate if 1,430 meters in thickness. At the corresponding point there is this deficiency of mass below sea level. There are two “Schweresynklinale” (Heim’s term) or density troughs, separated by a “Schwereantiklinal" or “Dichteschwelle.” This remarkable change of sign for the Bouguer anomaly is generally regarded as due to a voluminous, underground continuation of the gabbro, am phibolite, and allied heavy rocks exposed at the surface of the Ivrea zone. The conspicuous density-troughs tend to follow the topo graphic axes of Alps and Apennines, this tendency being somewhat less marked in the case of the Carpathians. Koss- mat’s map also shows excess of mass: below the regions sur rounding the Tyrrhenian Sea (between Italy and the Cor- sica-Sardinia line), including much of the western half of Italy; below the shores of the Adriatic; along the southern foot-slopes of the Alps; in the Pannonian basin; and under the wide plains of northern Germany and Poland. Testing Isostasy in Europe 201 Kossmat concluded that each mountain chain, like its foreland, is not isostatically compensated if regarded by it self alone, but that each whole region, including both moun tain chain and its foreland, is so compensated. He thought that the depressed belts adjoining the mountain chains (.Randsenken) are held down by the weights of the respec tive, rigidly connected mountain masses, so that each chain is undercompensated and each peripheral, sunken belt is overcompensated. According to his metaphor, the Rand senken act as “Schwimmgiirtel,” life-belts, for the mountain chains. Alps and foreland are rigidly held together, act as a unit, and as a unit are in isostatic balance with the rest of the lithosphere. Kossmat shared Heim’s belief in the sup port of the Alps by a deep root. Kossmat also gave his considered opinion that the crust- blocks typified by the Vosges and the Black Forest represent masses in excess or uncompensated loads on the lithosphere. In his book on isostasy and measurements of gravity, Bom expresses general agreement with Kossmat’s views but notes that the strong positive, free-air anomalies character izing the Alpine region still need explanation.9 R. Schwinner has published two papers dealing with the validity of the Airy explanation of isostasy in the eastern Alps. He concluded that this hypothesis accounts in part for the observed facts, but needs supplementing. The hori zontal variation of the Bouguer anomalies (g"0 — y 0) along cross sections of these mountains is so rapid that we must postulate important disturbing masses much nearer the sur face than the actual Airy “roots.” Schwinner suggested that some of the higher disturbing masses are thick, more or less vertical injections of simatic material, reaching well up into the sial; and that other gravitational disturbances are occasioned by the continuation of the relatively dense rocks of the Bohemian massif across the Alpine belt and beneath its nappes.10 202 Testing Isostasy in Europe Two years later, in the same journal (vol. 29, 1931, p. 352), Schwinner announced a similar thesis concerning a belt of the eastern Alps, that traversed by the Tauern road and a parallel profile that extends from Rauris through the Sonnblick to Ober Drauburg. Here the high-level masses include the Tauern granite and certain voluminous schists, all less dense than the normal sial, but the dominant control over the values of gravity is assigned to the negative masses represented in the Airy “roots.” Computation of the effects of the roots was simplified by assuming these to be a single root, composed of horizontal, rectangular layers in steplike arrangement. From Schwinner’s arguments it would appear that the eastern Alps are not in isostatic equilibrium. The Drau and Berchtesgaden portions of the area have excess mass and are characterized by “secular” subsidence. On the other hand, the Tauern portion and that of the Carinthian lakes show defect of mass, and have recently been rising. Schwinner further concluded that, in this last orogenic phase, vertical movements, rather than horizontal, are ruling.
After Heiskanen had shown that the Airy hypothesis ex plains observed gravity in the Swiss Alps as well as, or some what better than, the Pratt-Hayford hypothesis, another Finnish geodesist, E. Salonen, calculated the thicknesses of the Airy roots under Switzerland.11 As a basis he used the same principle that Helmert employed when determining the sea-level thickness of the lithosphere at steep-to coast lines. See p. 54. Between Lake Geneva and Lake Constance the lines join ing points of equal Bouguer anomaly run closely parallel with the orographic axis and geological strike of the moun tain system. The subterranean disturbing mass under the Testing Isostasy in Europe 203 Alps must, therefore, be here elongated in the same direc tion. Salonen selected for study six sections, all nearly at right angles to the Alpine axis. He assumed that the Airy
Figure 39. Salonen’s section of the Alps, illustrating his method of estimating the thickness of the root. compensation in each profile is composed of a bundle of rec tangular, indefinitely long, horizontal prisms, which are arranged at right angles to the section. The attractive effect of each prism on gravity at geoidal level was computed, 204 Testing Isostasy in E urope and the sum of such effects found. By a succession of trials for each cross-profile, Salonen deduced the sea-level thick ness of the sial that would best explain the Bouguer anom alies encountered along that profile. The relief was considered in the simplified form repre sented in Niethammer’s map of average heights in Switzer land, the unit area for averaging height being a square of 8 kilometers on the side; the contour interval was made 200 meters. Salonen states that this treatment of the topog raphy must give more trustworthy results for his problem than if the actual, endlessly varied relief were directly con sidered. The densities of sial and sima were assumed to be 2.7 and 3.0 respectively. The calculated thickness of sial would be nearly the same as when values of 2.7 and 3.1 were taken. The curvature of the earth was found to have a negligible effect. The result for one of the cross-profiles is illustrated in Figure 39, which refers to the section passing near the Jung frau. Five other profiles were similarly figured in the origi nal paper, all with a similar kind of pattern and meaning in principle. The best sea-level thickness of the sial came out at 26 kilometers. Since the mean height of the Alps above sea level, in the region investigated, is 1,500 to 2,000 meters, the additional thickness of the sialic root is 13 to 18 kilometers, if the difference of density for sial and sima is 0.3. Hence the total thickness of the sial in the region is 39 to 46 kilo meters. In his 1924 study Heiskanen had deduced 41 kil ometers for the Alps in general. Seismological evidence favors a value not greatly different.12 With Helmert’s 1901 formula for the reference spheroid, the mean isostatic (Airy) anomaly was found to be +9 milligals—equal to about —3 milligals if computed from the International spheroid. Testing Isostasy in Europe 205 The pendulum evidence for the close approach of Switzer land to isostatic equilibrium has been corroborated by Niethammer’s recent report on the slopes of the geoid in this region, as determined directly by the plumb-line method. He found that in a north-south section through Mont St. Gotthard the geoid rises no more than about 2.3 meters above the spheroid. This is a striking result in view of the extraordinary abundance of data available for this particular investigation, and in view of the fact that the rocky surface of the belt ranges from 500 to 3,000 meters above sea level.13
H E ISK A N E N ’S STU D IES The 1924 paper of Heiskanen, already noticed, was largely concerned with gravimetry and isostasy in continental Eu rope.14 He first computed the Hayford anomalies for many European stations, with the help of tables which had been prepared by the United States Coast and Geodetic Survey, and then found from the Hayford anomalies the corresponding Airy anomalies by applying factors specially determined by Heiskanen himself. All anomalies were computed from Helmert’s 1901 spheroid. Ca u c a s u s . Among the observations discussed were those that had been made in the Caucasian region (63 sta tions). Here, for each station, nine different kinds of anom aly were calculated, the kinds being described as follows:
(1) Free-air; (2) Bouguer; (3) Pure-topographic—taking account of the topog raphy of the whole earth; (4) Hayford, with depth of compensation at 113.7 kilometers; (5) Hayford, with depth of compensation at 156.3 kilometers; (6) Hayford, with depth of compensation at 184.6 kilometers; 206 Testing Isostasy in Europe
(7) Hayford-rcgional, with depth of compensation at 113.7 kilometers and regional compensation to a radius of 166.7 kilometers (outer limit of zone O); (8) Airy, with sea-level thickness of the crust (sial) at 77.2 kilometers, and with difference of density be tween sial and sima at 0.2; (9) Airy, with sea-level thickness of the sial at 63.8 kilometers, and with difference of density between sial and sima at 0.3. In seven cases the mean anomalies are given in Table 27, which also states the means for 50 stations, for which Heiskanen later published the anomalies based on the 1930 International spheroid.*
T able 27 MEAN ANOMALIES FOR THE CAUCASIAN REGION (milligals)
a b C d Means, 63 stations Variation from Means, 50 stations Kind of anomaly (Helmert formula) mean, col. b (International formula) 1. Free-air + 26 46 + 16 2. Bouguer -60 31 -84 4. Hayford (T = 113.7 km) + 53 27 +46 5. Hayford (T = 156.3 km) +49 24 +38 7. Hayford-regional +55 26 +44 8. Airy (D = 77.2 km) +45 22 +33 9. Airy ([D = 63.8 km) + 50 22 +39
Heiskanen developed expressions showing how the anom aly of each type varies linearly with height of station (H), and thereby was led to a criterion for the best method of re duction. The Caucasian data (Helmert spheroid) gave the following formulas (error terms omitted), where D = Hayford depth of compensation; T = thickness of “crust” or sial: * See W. Heiskanen, “Handbuch der Geophysik,” Berlin, vol. 1, 1934, p. 901. The 13 stations missing from the 1934 list include nine in the Black Sea region. Testing Isostasy in Europe 207 Kind of reduction Value of anomaly (milligals; H in kilometers) Free air...... — 0.037 + 0.062 X H Bouguer...... — .039 — .042 X H Hayford (D = 113.7 km)...... + .024 + .023 X H Hayford (D = 156.3 km)...... + .024 + .015 X H Hayford (D = 184.6 km)...... + .024 + .010 X H Airy (T = 64 km)...... + .033 + .005 X H Airy (T = 77 km)...... + .032 + .000 X H The best mode of reduction is that which brings the term with H nearest to zero in value. For the Caucasian region, this criterion favored that one of the Hayford hypotheses which assumed the depth of com pensation to be 184.6 kilometers, but the actual values of observed gravity would be still better explained if the depth be taken at 250 kilometers. The Hay ford-regional reduc tion (7) gave a decidedly better result than (4) or (5). Still somewhat better for the Caucasian region are the re sults from the two Airy hypotheses, especially from that which assumes the sea-level thickness of the sial to be 77 kilometers. By extrapolation Heiskanen deduced a range of from 77 to 104 kilometers for the thickness of the sial un der the Caucasus, if in isostasy. Outside the Caucasus, Heiskanen had 97 European sta tions with measured data. From their study he was led to the following conclusions: (1) contrary to general opinion, the Harz and Riesengebirge regions are in close isostatic balance; (2) the Alps and the bordering lowlands (Randsen- ken) are in the same state (the best Airy-root thickness un der the Alps at about 41 kilometers); (3) the Mediterranean basin shows a positive overcompensation; (4) Spitsbergen is in close isostatic balance. In general, the Airy hypothesis fits the facts of Caucasus and Alps as well as, or somewhat better than, the Pratt- Hayford. We remember a similar result for the United States. It also appeared that the Hayford depth of com pensation can not be uniform over the face of the earth. 208 Testing Isostasy in Europe Heiskanen found that for the Airy hypothesis the thickness of the sial is much more important than the difference of density between sial and sima. For example, the result of computation is little affected if this difference be changed from 0.3 to 0.6. N orway. In Publication No. 5 of the Finnish Geodetic Institute, 1926, Heiskanen reported on anomalies at 46 Norwegian stations. From this paper Table 28, giving some essential results, has been abstracted.
T able 28 MEAN ANOMALIES IN NORWAY (based on Heiskanen’s 1924 triaxial spheroid; milligals)
Southern Norway (29 stations; Northern Norway (17 stations; average height, 176 meters) average height, 18 meters) Average Average Kind of anomaly Mean deviation Mean deviation anomaly from mean anomaly from mean Free-air - s 26 - l i 42 Bouguer -23 32 -12 41 Hayford (80 km) + 15 17 - 1 31 Hayford (120 km) + 10 18 - 5 32 Hayford (160 km) + 6 18 - 9 33 Hayford (200 km) + 3 19 -12 34 Airy (40 km) + 16 17 + 1 28 Airy (60 km) + 11 18 - 4 31 Airy (80 km) + 7 19 - 9 32 Airy (100 km) + 2 20 -13 34 In proportion to area, the stations are more numerous in southern Norway, and their anomalies were first discussed. The deviations of the free-air and Bouguer anomalies from their respective means are considerably greater than the analogous deviation for each type of isostatic anomaly. This showed that “isostatic compensation dominates in southern Norway.” It may be noted that, if reductions had been based on the 1930 International formula for the earth’s figure, each mean would have been little changed. Heiskanen then examined the relation between anomaly T esting Isostasy in Europe 209 and elevation of station, again in southern Norway. The linear functions deduced are as follows: Value of anomaly as function of height Kind of reduction of station (milligals; H in kilometers; International formula) Free-air...... — 0.006 + 0.038 X 3 Bouguer...... — .003 — .080 X H Hayford (80 km)...... + .021 + .000 X H Hayford (120 km)...... + .019 - .011 X H Hayford (160 km)...... + .016 - .019 X H Hayford (200 km)...... + .014 — .026 X H Airy (40 km)...... + .024 - .008 X H Airy (60 km)...... + .021 - .020 X H Airy (80 km)...... + .018 - .029 X H Airy (100 km)...... + .014 — .035 X H For both the free-air and Bouguer reductions, the term depending on height is larger than the average error, but for all the other reductions it is smaller. Herein is a second reason for crediting the dominance of isostatic compensation. Since the most probable depth of compensation (Hayford) or thickness of sial (Airy) is that which causes the term de pending on height to disappear, it was concluded that the Hayford depth of compensation is about 80 kilometers, and the sea-level thickness of the sial (Airy) about 32 kilometers. The average elevation of the mountains of southern Norway being approximately 1,000 meters, a thickness of sial under them comes out at 37 kilometers, or, excluding the observa tions at the exceptionally high Finse station, 39 kilometers. Moreover, the sum of the squares of mean error is much smaller in the case of each isostatic reduction than in the case of either the free-air reduction or the Bouguer reduc tion; hence additional corroboration of belief in a relatively close degree of isostasy. A definite choice between the Hayford and Airy types of compensation could not be made, but Heiskanen preferred the latter because it agrees with seismological evidence. In general, northern Norway led to similar conclusions re garding compensation, but the two large anomalies (i.e., + 59 and + 125 milligals, with Hayford depth of compen 210 T esting Isostasy in Europe sation at 80 kilometers) on the Lofoten Islands prove a great excess of mass there—perhaps represented by gabbro, dia base, or a ferruginous formation. Heiskanen concluded that the data available in 1926 were insufficient to test the question whether the glaciated tract of northwestern Europe is still out of isostatic balance be cause of delay in the recoil of the lithosphere after the last deglaciation of the region.
GRAVITY IN FINLAND On the cause for the demonstrated post-Glacial upwarp- ing of northwestern Europe, much light has since been thrown by reports of U. Pesonen and R. A. Hirvonen on measurements of gravity in Finland, which lies wholly within the zero isobase of contemporary uplift. Pesonen’s paper is No. 13 of the Veroffentlichungen des Finnischen Geoddtischen Institutes, 1930; Hirvonen’s is No. 24 in the same series, dated 1937. Pesonen, using Helmert’s 1901 spheroid of reference, gives observed gravity (Helsinki base station, based on Potsdam), free-air anomalies, and Bouguer anomalies at 111 stations. Since the region has slight relief, he did not think it worth while to compute the isostatic anomalies, for which inde pendent corrections, to take account of assumed compensa tion, are not likely to exceed one milligal. The mean anomalies with regard to sign were found to be, in milligals: Ilelmert International formula formula Free-air anomaly - 7 - 17 Bouguer anomaly - 14 - 24 Range of free-air anomalies - 50 to + 41 - 60 to + 31 Pesonen was struck by the comparatively low values of gravity over the extensive Rapakivi granite of southern Fin land, between Helsinki and Viipuri, and suggested, among conceivable explanations, the idea of crust-warping, whereby Testing Isostasy in Europe 211 the lighter sial with normal thickness was depressed under the Rapakivi granite when the great eruptive body was em placed. This hypothesis recalls the question whether the erupted mass is a lopolith, or, alternatively, the filling of a fault-trough. The case also has a bearing on Glennie’s con ception that crust-warping is one of the general reasons why we have broad areas of one-sign anomaly. (See p. 243.) In 1937 Hirvonen reported on 91 additional stations in Finland and added data from 56 Russian stations, distrib uted along a nearly north-south belt extending from Lake Ladoga to the Arctic Ocean, north of Kola. In two respects the anomalies were computed on a basis different from that assumed by Pesonen. First, Hirvonen replaced the Hel- mert spheroid of reference with the International spheroid of 1930; and, secondly, he replaced Pesonen’s assumed value of gravity, 981.910 milligals, at the Helsinki base station by the improved value of 981.915 milligals. With regard to sign the mean free-air and Bouguer anom alies, computed from Hirvonen’s table and map, are given in the first two rows of the following table:
For 202 Finnish For 263 Finnish and stations Russian stations Free-air anomaly — 7.4 milligals —4 milligals Bouguer anomaly — 15.7 milligals — Mean elevation 73.5 meters — Range of elevation 1.6 to 261 meters —
Hirvonen’s results will be reviewed again in chapter 10, where it will be noted (Table 52) that each mean anomaly becomes about 9 milligals more negative when the compu tations are based on Heiskanen’s 1938 triaxial figure of the earth.
GRAVITY MEASUREMENTS IN CYPRUS The island of Cyprus represents a thoroughly abnormal 212 Testing Isostasy in Europe field of geoidal warping and corresponding gravity anomaly. The existence of strong deflection residuals in the plumb-line study was proved by the Hydrographic Department of the British Admiralty. This fact led C. Mace to measure the intensity of gravity at 13 stations, with a range of height above sea level between 3 meters and 1,298 meters. He also computed the gravity anomalies.15 The free-air anomalies range from + 75 milligals to + 282 milligals, and average +172 milligals. The Bouguer anom alies range from + 73 to + 174, and average + 126 milli gals. The Hayford (T = 113.7 km) anomalies range from + 43 to + 173, and average + 105 milligals. The Airy (D = 40 km) anomalies range from + 48 to + 174, and average + 102 milligals. The free-air anomalies are “among the largest ever found,” and the isostatic anomalies at two stations are “the largest positive anomalies ever found.” As the isostatic anomalies “change by a large fraction of themselves in distances of the order of 20 kilometers, the masses responsible for them cannot be situated at a very great depth.” In spite of the great, unbalanced load of rock existing un der Cyprus, the island seems to have undergone no subsi dence for at least the last 2,000 years. Mace writes: “Raised beaches show that the land has risen considerably relative to the sea since the Pleistocene.” But from the incomplete accounts of the geology of the island, by Bellamy and Jukes Brown, Reed, and Philippson, it appears more probable that the uplift was really of late Pliocene date. Moreover, none of these five authors has considered the possibility that some at least of the “raised beaches” register merely a Pleis tocene, eustatic drop of sea level—contemporaneous with that represented along great stretches of the main Mediter ranean shores. Emergence of that type must, of course, be distinguished from uplift of the land. More work needs to be done on the so-called raised beaches before we can be Testing Isostasy in Europe 213 assured of any important vertical movement of Cyprus dur ing the last million years. From Mace’s table of anomalies and from his map, it ap pears that we have here a sector of the earth, measuring more than 225 kilometers in length and 100 kilometers in width, and bearing an uncompensated load about equal to that of one kilometer of granite, spread evenly over the sec tor. Mace leaves open the question whether such a load can be borne by the lithosphere alone, but concludes that the existence of such large positive anomalies in a region that seems to have no tendency to subside shows on how insecure a basis the alleged connection between the negative anomalies and the rising coast line in Scandinavia rests; and shows that the viscosity of the lower layer calculated therefrom may be entirely erroneous. However, we shall see in chapter 12 that this conclusion may well be doubted when due allowance is made for the vast difference in the spans of the loads represented in Cyprus and Fennoscandia. The cause of the Cyprus field of one-sign anomaly is a problem for the future; a geologist naturally thinks of one possible cause—the disturbance registered in the formation of the adjacent Taurus Mountains. ADDITIONAL EUROPEAN DATA Heiskanen’s world Catalogue is a mine of information bearing on isostasy and therefore on the distribution of strength in the earth. From the tables in this volume the present writer has calculated the mean anomalies (based on the International formula) of gravity in various parts of Europe, other than those already considered. The results are given in Tables 29 to 32, referring to areas in central Eu rope, Italy, Lithuania, and Russia. The full meaning of these tables will not here be discussed; their entry is pri marily intended to add to the general record of facts on 214 Testing Isostasy in Europe which constructive thought regarding terrestrial strength must be based. T able 29 MEAN GRAVITY ANOMALIES IN CENTRAL EUROPE (Latitude 47° to 52°; east longitude 7° to 24°. T, depth of Hayford compensation; D, sea-level thickness of the sial. Milligals.)
Average Hayford Airy eleva anomaly, T — anomaly, D = Region tion of Free-air Bouguer stations anomaly anomaly (meters) 80 km 113.7 km 40 km 63.8 km Harz Mts (11 stations) 417 +52 + 9 +36 +34 +36 +33 Riesengebirge (8 stations) 717 +45 -29 + 11 + 8 + 11 + 6 North of the Alps (10 sta- tions) 452 - 9 -52 + 13 + 12 + 19 +19 Elsewhere in central Eu- rope (13 stations) 178 + 9 - 9 + 19 + 19 +22 +22
T able 30 MEAN GRAVITY ANOMALIES IN ITALY (Latitude 38° to 45°; east longitude 9° to 18°. 14 stations. Milligals.) Average elevation Free-air Bouguer Hayford anomaly (meters) anomaly anomaly (!' = 120 km) 221 +53 +42 +63 Heiskanen is inclined to attribute the strong positive qual ity of the Italian anomalies to the fact that the peninsula is the locus of widespread volcanism, but it is hard to see how that can be a sufficient explanation.
T able 31 MEAN GRAVITY ANOMALIES IN LITHUANIA (Latitude 54° to 46°; east longitude 21° to 26°. IS stations. Milligals.)
Average Free-air Bouguer Hayford anomaly, T — Airy anomaly, D = elevation anomaly anomaly (meters) 113.7 km 40 km 80 km 120 km 20 km 40 km 60 km 75 -0.5 -8.8 -2 -1.3 -1.7 -2.4 -0.7 -1.5 -1.9 Table 31 shows how nearly alike are the anomalies com puted on a wide range of assumptions regarding kind and T esting Isostasy in Europe 215 depth of compensation, when the region in question is as low and featureless as the Lithuanian plain. It is also worth noting that the negative character of each isostatic anomaly does not agree with the idea that there is any appreciable bulge of the lithosphere outside the hinge-line of Witting’s map showing the contemporary uplift of Fennoscandia; Lithuania is situated in this exterior, peripheral zone. (See p. 321).
T able 32 MEAN GRAVITY ANOMALIES IN RUSSIA (milligals)
Average Free-air Region elevation anomaly Hayford anomaly (meters) Around Saratov (latitude 51°+; longitude 47° + ). 12 stations. 68 -2 4 -23 (T = 113.7 km) Ural Mountains (latitude 54°+; longitude 59°±). 22 stations. 351 + 17 + 16 (T = 113.7 km) Crimea (latitude 45° — ; longitude 34°+). 16 stations. 227 +84 +51 (T = 120 km)
REVIEW AND FORECAST The networks of gravity stations in Europe are largely national, and many regions are not covered at all. Hence reliable isanomaly maps are confined to small fractions of the whole continent, and the detection of the maximum un compensated load on this earth-sector is a job for the future. And, besides political disunion, there is another reason why the study of such loads has not advanced as in India or the United States. Many of the European geodesists and geo physicists have been slow to recognize the full value of the isostatic hypothesis and to be actively interested in testing its truth. This is not the case with the workers in Switzer land and Finland, who have already presented models of achievement in our field of study. Notwithstanding the lack of any systematic examination of a single area covering a million square kilometers or more, 216 Testing Isostasy in Europe the observations made in Europe indicate uncompensated loads of the same order as those deduced in North America east of the Rocky Mountain front. The greatest reported loads, with respect to both span and maximum intensity, seem to be those of the Caucasus, some of the horsts of cen tral Europe, Cyprus, and perhaps some areas in Russia. The Alps as a whole are not far from perfect equilibrium. The most suggestive of the researches relevant to the dis tribution of terrestrial strength is that centering in Finland and representing admirable co-operation among geodesists, geologists, and hydrologists. The unique value of the Fin nish and Swedish observations will be emphasized in chap ters 10 and 12. While the European geodesists have been handicapped for gravitational study of their own continent, it should be noted that they have led in the investigation of two other continents, Africa and Asia, as well as the oceanic areas. The next two chapters will be concerned with these sectors of the globe, where the European explorers have secured gravitational data of the greatest importance.
R e fer en c es 1. E. Borrass, Verhand. Konf. Internat. Erdmessung, sessions of 1903, 1906, 1909, and 1912. 2. G. Costanzi, Rivista geog. Ital., vol. 14, 1907, p. 364. 3. W. Deecke, Neues Jahrb. f. Mineralogie etc., Festband, 1907, p. 129. 4. Compare F. Kossmat, Abhand. math.-phys. Klasse, Sachs. Akad. Wissen., vol. 38, 1920, p. 10. 5. W. Heiskanen, Annales Acad. Sci. Fennicae, ser. A, vol. 51, No. 10, 1939. 6. A. Heim, “Geologie der Schweiz,” 1921, vol. 2, p. 54. 7. F. Kossmat, Die Medilerranen Kettengebirge in ihrer Bezie- hung zum Gleichgewichtszustande der Erdrinde (Abhand. math.-phys. Klasse, Sachs. Akad. Wissen., vol. 38, No. 2, 1920, pp. 1-62). Testing Isostasy in Europe 217 8. F. Kossmat, op. cit., p. 16. 9. A. Born, “Isostasie und Schweremessung,” Berlin, 1923, p. 75. 10. R. Schwinner, Gerlands Beitraege zur Geophysik, vol. 23, 1929, p. 35. 11. E. Salonen, Annales Acad. Sci. Fennicae, ser. A, vol. 37, No. 3, 1932. 12. V. Conrad, Gerlands Beitraege zur Geophysik, vol. 20, 1928, pp. 257, 276; B. Gutenberg, “Handbuch der Geophysik,” Berlin, vol. 1, 1934, p. 541. 13. T. Niethammer, Bull. 20, Schweiz. Geodat. Komm., 1939. 14. W. Heiskanen, Veroffent. Finnischen Geodat. Inst., No. 4, 1924; see particularly pp. 15, 29, and 60-79. 15. C. Mace, Mon. Not. Roy. Astr. Soc., Geophys. Supp., vol. 4, 1939, p. 473. 8 TESTING ISOSTASY IN AFRICA AND ASIA
Except for a few limited areas, each of the two most ex tensive continents still awaits systematic work on deflections of the vertical and on the intensities of gravity. Yet extra ordinarily significant investigations have already been made in the Rift belt of East Africa, Siberia, India, Turkestan, and Japan. Some of the leading results of these studies will now be noticed, with special attention to India, the most thoroughly and systematically examined among all the larger continental domains.
EARLIER WORK IN EAST AFRICA In 1911, Kohlschiitter published the free-air, Bouguer, and isostatic (local compensation) anomalies for 35 stations dis tributed over the plateaus and grabens (fault-troughs) of the territory then known as German East Africa. The mean isostatic anomaly at the 12 graben stations came out at — 52 milligals and that for 12 plateau stations at —20 milli- gals (Helmert 1901 formula).1 This contrast prompted Stackler to recalculate the isostatic anomalies on the assump tion that the compensation is here regional, each fault-block as delimited in Krenkel’s geological map being in equilibrium with all neighboring blocks, but not itself endowed with local compensation.2 The result was to reduce the mean isostatic anomaly from —52 to —37 milligals, the mean for the pla teau stations being almost unchanged. 218 Isostasy in Africa and Asia 219 In 1923, Born discussed the geological meaning of these conclusions.3 He adopted the prevailing view that the grabens are forms of collapse in a region which was subject to horizontal tension and fracture. Two possibilities were conceived, according to whether the graben blocks slipped down along fault-fractures which did or did not reach down far enough to tap eruptive magma. In the first case, allow ance would have to be made for the extra attraction of the relatively dense igneous rock that entered, and perhaps spread out from, the fractures and froze there. Born points out that long stretches of the grabens show no sign of the imagined eruptivity. The second of the two modes of producing abnormalities in the field of gravity was therefore thought to be the more probable explanation of the negative anomalies at the graben stations. On the other hand, Born was inclined to account for the positive anomalies (gQ — ya) at coast stations along the southern part of the Red Sea, and also for the positive anomalies found there by Hecker on board ship, by postulating the eruption of large volumes of dense igneous matter in this area. Born’s general conclusion was like that of Kohlschiit- ter: in some parts the East African grabens are fully compen sated, while other parts are almost wholly uncompensated.
BULLARD ON GRAVITY IN EAST AFRICA The most thorough test of isostasy in the Rift region of East Africa is that by E. C. Bullard, whose presentation is a model of clear, concise, and illuminating treatment.4 The Bullard party measured gravity at 57 points, distributed over a million square kilometers of plateau and rift valleys. Kohlschiitter’s measurements at 30 additional stations in the same region were also included in Bullard’s discussion. The anomalies were based on the 1901 Helmert spheroid of reference, but their weighted means are also stated in terms of the 1930 International formula. The kinds of anomaly 220 Isostasy in Africa and Asia actually computed are the free-air, Bouguer, Hayford (depth of compensation at 113.7 kilometers), and Airy (called “Heiskanen” by Bullard) with sea-level thickness of the sial taken at 40, 60, 80, and 100 kilometers respectively. For all 87 stations, the various observations being given equal weights, the means of the isostatic anomalies (Inter national formula) were found to be, in milligals:
Airy, thickness of sial (km) Hayford (113.7 km) 40 60 80 100 With regard to sign - 8 - 3 - 1 1 -18 -24 Without regard to sign 21 20 20 23 27 When, however, the anomalies of each kind were weighted so as to allow only one value of observed gravity for each square degree of the earth’s surface actually traversed, the means with regard to sign come out with the values shown in columns 2 and 3 of Table 33.
T able 33 WEIGHTED MEAN ANOMALIES, ALL STATIONS (milligals; International formula)
1 2 3 4 Per Heiskanen Kind of anomaly Per ITelmert Per International triaxial formula formula formula of 1938 Free-air + 12 -7 +3 Bouguer -118 -137 -127 Hayford (113.7 km) - 7 -26 -16 Airy (40 km) - 3 -22 -12 Airy (60 km) -1 0 -29 -19 Airy (80 km) -1 6 -35 -25 Airy (100 km) -22 -41 -31 Column 4 gives the approximate means when referred to Heiskanen’s new spheroid of reference with a longitude term, values calculated by the present writer.* * Bullard (p. 519 of his memoir) compared his results with those expected if Isostasy in Africa and Asia 221 From the relation of the Bouguer anomalies to the eleva tions of the stations, Bullard concluded that “the plateau of Africa is underlain by a deficiency of density which produces a deficiency of gravity about equal to the attraction of the visible topography. That is to say, it is isostatically com pensated.” That the topography as a whole is nearly compensated is shown also by the mean values of the isostatic anomalies, considered both with and without regard to sign. By two methods, 60 kilometers was found to be close to the most probable thickness of the “earth’s crust” (sial) un der the East African plateau, if each piece of topography be assumed to have its compensation immediately under it. But Bullard adds (p. 521 of his memoir): Since the crust has a finite strength, the topographic loads will cause it to bend downwards into the underlying magma and the compensation will be spread over a horizontal distance of the order of 50 kilometres. It is easy to see that the attraction of this distributed compensation is the same as that of a localized compensation at a greater depth. The above estimate of the crustal thickness is therefore too great; the reduction required is of the order of 50 per cent. We therefore conclude that the gravity data are consistent with a crustal thickness of about 30 kilometres, but that anything between 20 and 60 kilometers can be made to fit the data nearly as well. This value is consistent with the assumption made on page 509 that the matter produc ing the anomalies over the Rifts is situated at the lower surface of the crust; for it was shown that this matter could not lie deeper than 35 kilometres. As was to be expected, Bullard corroborated Kohlschiit- ter’s discovery that the Rift valleys are uncompensated. The general fact is illustrated in Figures 40 and 41. In the earth’s figure had the longitude term of Heiskanen’s older, 1924 and 1928, formulas (see Table 2), which would “require gravity to be slightly in excess in E. Africa.” Since gravity is there deficient, Bullard doubts the triaxiality of the mean figure of the earth. This particular objection to the idea of triaxiality does not, however, apply in the case of the Heiskanen formula of 1938. 222 Isostasy in Africa and Asia Figure 40 (a copy of Figure 10 in Bullard’s memoir) the line of variation for the Hayford anomalies is substantially coin Milligals Meters cident with the corre 2000 sponding line for the Airy anomalies. The curves would be almost un changed if the assumed normal density of surface rock were changed from Leuel 2.67 to 3.0. Bullard discusses the distribution of the mat ter responsible for the strong downward curva ture of the lines of anom aly across the Rifts: F igure 40. Gravity profile across Lake Albert, African Rift. The dip in the Bouguer anomalies shows that not only is the Rift uncompensated, but that there is more light matter under it than if it was simply cut out of the plateau leaving the compensation unchanged. . . . Milligals Meters
+ 100
*Sea
- 100
-200 F igure 41. Gravity profile across Lake Tanganyika, African Rift. The gravity data show that the Rift is underlain by light matter at a depth of less than 35 kilometres, but cannot decide Isostasy in Africa and Asia 223 whether the light matter is near the surface or near the bottom of the crust. That it is unlikely to be near the surface may be deduced from the geology of the Rifts. It has been conclusively shown that the floor of the Rift has been lowered relative to the sides between parallel faults and that the rocks underlying the floor are similar to those forming the plateaux on each side. In the Lake Albert section the floor is covered with sediments of unknown thickness brought down by the Semliki, and it might be argued that the lightness of these sediments was the cause of the anomaly. This, however, is unlikely; first, because there is no reason to suppose that the sediments are of the enormous thickness necessary (2.5 kilometres for a density of 1.8); sec ondly, if they were of the requisite thickness, it seems unlikely that they would maintain their low density to a depth of more than a few hundred metres; and thirdly, a similar gravity defi ciency is found at Magadi on the floor of the eastern Rift where bare rock is exposed at the surface. It is therefore thought that the light matter is deep-seated, and it seems natural to suppose that it is situated at the bottom of the crust and consists of a pro jection of crustal matter into the underlying magma. Concerning the structure of the Rifts: The plateau of Africa has been shown to be in approximate iso static equilibrium, that is, the downward force of gravity on the mass of the plateau is balanced by the upward thrust of the underlying magma on the root of light crustal matter projecting into it. Under the Rifts there is an excess of light matter and the upward hydrostatic forces will exceed the downward pull of gravity; the floor of the Rifts will therefore rise unless held under by some other force. This much may be deduced directly from the observations and from the usual interpretation of isostasy; to proceed further we must examine the possibilities suggested by the geology of the region and see which of them are compati ble with the state of affairs revealed by the gravity measure ments. After rejecting Gregory’s well-known “fallen keystone” hypothesis and also Wegener’s “rent” hypothesis, Bullard expresses more satisfaction with Wayland’s hypothesis of fracture and reverse-faulting under excessive horizontal 224 Isostasy in A frica and Asia compression of the lithosphere. However, this third hy pothesis itself, according to Bullard, needs supplementing, and he concludes that “the most likely explanation is a fold ing downwards of the lower part of the crust accompanied by a breaking of the upper parts.” (Bullard, pp. 510, 517.)
GRAVITY IN SIBERIA The geodesists of the U.S.S.R. have measured gravity at 357 Siberian stations, and the reductions have been made by P. M. Gosschkoff.5 The free-air and Hayford (T = 113.7 kilometers) anomalies have been entered in the world Cata logue. The stations lie within an area bounded by the 44th and 57th parallels of latitude and by the 73rd and 92nd meridians of east longitude. The mean Hayford anomaly is —3.4 milligals, a value close to the mean for 448 United States stations, namely —5 milligals (same reference for mula [international] and depth of compensation [113.7 kilo meters]). (See Table 19, p. 161.)
CONDITIONS IN INDIA For more than a century, the Survey of India has been accumulating records of quite special meaning in the prob lem of terrestrial strength. In 1843 Everest was able to re port on the great meridional arc traversing the peninsula. While the field program, with the plumb-line method, was under way, it became evident that High Asia, including the Himalayas, did not attract the plumb bob as much as that extra rock above sea level should attract it. We have seen that Pratt and Airy explained this fact in two different ways. Airy’s statement was less vague than that made, also in 1855, by Pratt, and was more in line with modern ideas regarding the constitution of the lithosphere; hence Airy has been called “the father of isostasy.” Nevertheless, India, among all the extensive regions with relatively close networks of plumb-line and gravity stations, is being regarded by some Isostasy in Africa and Asia 225 high authorities as departing so far from isostasy that one should no longer recognize a principle of isostasy at all. Whether this drastic conclusion is justified is a vital ques tion. We shall review it in the light of the facts discovered during many decades of triangulation work, and then in the light of facts won at more than 400 gravity stations. The Geoid in India. Everest showed that, south of a certain point in his meridional arc, the vertical is displaced in the sense opposite to that expected by the attraction of High Asia. The (northward) deflection of the vertical in the region south of that point could not be referred to the pull of any visible, uncompensated topography still farther south, for peninsular India, a peneplain with relatively small residual hills, departs but little from the normal relief of a continent. The extra southward pull on the plumb bob over a belt immediately south of the Indo-Gangetic plain of alluvium (Figure 42) was therefore attributed to a wide-
F igure 42. Section through the Ganges alluvium (after Wadia). spread, subterranean mass crossing middle India. To the subterranean mass Everest gave the name “Hidden Cause.” The existence of this broad belt of mass in relative excess, extending across middle India from the Arabian Sea to the Bay of Bengal, has been abundantly confirmed by ten dec 226 Isostasy in Africa and Asia ades of subsequent geodetic research. We shall refer to the positive belt under the name “Hidden Range.” Since High Asia does cause a small, net, southward deflec tion of the vertical, contrary to the sense of the deflection over the northern flank of the Hidden Range, the wide belt containing the Indo-Gangetic alluvium is a gravitational trough. This second part of the gravity field was visualized by Everest. He also saw that south of the Hidden Range the plumb line was deflected again to the northward, in such fashion as to prove the Hidden Range to be only a few hun dreds of miles in (meridional) breadth. Everest had insuffi cient data to complete the deflection pattern to Cape Com orin, the southern point of the peninsula. The field ob servations of recent years have shown that the southern third of the peninsula represents a second gravity trough. At first it was thought that the deflection of the plumb line from the position fixed at each station by the chosen ellips oid of reference grew gradually less, until the deflection be came zero near Cape Comorin. However, further field study led to the conclusion, announced in the 1934 Report of the Survey, that the southern trough is broader and ex tends well beyond the Cape. It is now clear, therefore, that Everest’s recognition of a general tripartite division of the field of gravity was in ac cord with the facts of Nature, though his data had been largely derived from a chain of stations in a single, meridional zone. Inasmuch as the vertical at any terrestrial point is exactly at right angles to the geoid at that point, it became ever more certain that the actual or “natural” geoid in pen insular India is rather systematically warped out of any ellipsoidal figure of the earth. This geoid rises highest along the axis of the Hidden Range, where there is a gravi tational “crest,” and sinks to lowest levels along the axes of the northern and southern “troughs.” All three axes are roughly parallel and are also roughly parallel to the tangent Isostasy in Africa and Asia 227 to the frontal curve of the Hima layan chain of mountains. (See Figure 1.) In 1917, Oldham published a noteworthy paper in which he correlated the geodetic observa tions with the geology of the peninsula and Himalayas. After a good statement of the nature of the geodetic evidence regard ing the general distribution of masses and work densities, he described a comparatively sim ple but effective way of estimat ing the gravitational effects of the visible Himalayas. The geo detic data led him to picture the maximum thickness of the Ganges alluvium as 15,000 to 20,000 feet, the maximum being located near the main bounding fault on the north, the thickness gradually decreasing in the southerly direction. Thus he assumed this geosynclinal prism to have the cross section of a wedge. Oldham accepted the conclusions of the geodesists: that the central, high Himalayas are overcompensated, the com 43. 43. Structure-gravity profile across the axes of the Hidden Range and Gangetic trough, India (after Oldham). pensation being in excess of the load; and that the outer Sub- igure Himalayas are undercompen F sated. The uncompensated part of the load in this second belt 228 Isostasy in Africa and Asia was thought to depress the belt occupied by the Ganges alluvium, where the corresponding expulsion of subcrustal material caused the gravity anomalies to increase in nega
tive value.* (See Figure 43.) The expelled material was driven southward, giving the excess of mass represented by the Hidden Range. * S. G. Burrard (Prof. Paper No. 17, Survey of India, 1918) came to a more extreme conclusion; he explained all of the negative anomaly over the Ganges alluvium as the effect of the low density and great volume of the alluvium. With the assumed density he estimated the maximum thickness of the alluvial prism at the highly improbable figure of 50,000 feet. Isostasy in Africa and Asia 229 In order to make the general result more easily visualized, Oldham adopted Fisher’s hypothesis that, before the oro- genic disturbance, the whole region was underlain by a “crust” with uniform thickness of 25 miles, the “crust” rest ing on a viscous liquid of greater density. During the mountain-making the “crust” was thickened into a great root, which now supports the Himalayan chain as a whole. The present conditions were illustrated by a transverse sec tion, reproduced (with unessential modifications) in Figure 43.6 The section, about 700 miles or 1,100 kilometers long, is drawn so as to show the actual curvature of the earth’s surface. Divisions A and C are zones of positive anomaly of gravity; divisions B and D are zones of negative anomaly. Thus Oldham was led to the idea of crust-warping; his ex planation of the warping differed from that later given by Glennie and Vening Meinesz. We return to our direct inspection of the facts of geodesy; they are most conveniently presented in graphic form. Figure 44 is a black-and-white copy of the Survey’s col ored map, showing in feet the deviation of the natural geoid (data of 1923) from the 1930 International ellipsoid of refer ence. The elevated (positive) area, corresponding to the Hidden Range, is stippled; the two depressed areas bear the contour lines but are otherwise left blank.* Apart from small errors in the integration from observed values and azimuths of the deflections, this geoid must be regarded as representing fact, a fundamental datum which is quite inde pendent of hypothesis of any kind. Glennie gives a profile of the natural geoid in a section running about N. 10° E. from Cape Comorin across the axes of the positive arch and main Gangetic trough and on to the mountainous region north of the Himalayas.7 The profile is reproduced in Figure 45, a, where the continuous curve * A similar map, based on observations made before 1937, is Chart VII in the 1936 Report of the Survey of India. In principle, the two maps tell the same story. 230 Isostasy in Africa and Asia portrays deviations from the International ellipsoid, and the adjacent broken curve does similar duty when the deviations are referred to the “Survey of India Spheroid II,” which has
been adopted as best fitting the Indian observations. The positive part of each curve is a graphic indication of the “Hidden Cause” or “Hidden Range.” Since Figures 45, a and 45, b were published, it was discov ered that south of the Hidden Range the geoid does not rise
Depth S e a / e v e f (feet)
Granitic Layer (density 2.67) Norma! Surface __of J.Qterm_edjate_ Layer ( 33,000') • 40,000
Intermediate Layer (density 2.85)
- 60,001)
Normal Surface of "D unite” Layer ( too.ooo1) mniiinmMiiTmiffmifnriiTrmifmTiinniirmnuTTniTra~^- — — — •
“ Dunit®" ( d e n s it y 3 .3 0 ) F igu re 45, b. Glennie’s section of crust-warps assumed to explain the curvature of the geoids shown in Figure 45, a. so steeply as shown in Figure 45, a, the geoid being depressed below the spheroid all the way to Cape Comorin and Ceylon. Nevertheless, the drawings illustrate the principle of crust- Isostasy in Africa and Asia 231 warping as applied to the main features of the Indian field. Later Bomford published a north-south section between latitudes 8° and 17° north, showing the topography and the relations of both the natural geoid and the compensated geoid to the International ellipsoid. This section is repro duced in Figure 46, where it is seen that the natural geoid, throughout this wide stretch of southern India, is consist-
Figure 46. Bomford’s section of India, showing geoids and topography. ently below the ellipsoid; and that the two geoids are, in gen eral, not far from coincidence.8 Having a map of the natural geoid in hand, Hunter asked this question: How would the geoidal surface have to be changed if Hayford’s type of isostasy prevails in India? If the topography is exactly compensated in the Hayford man ner, then the sea level, continued under Indian land, should be part of some ellipsoid which is devoid of extensive, and at the same time strongly marked, humps and hollows. In order to test Hayford’s hypothesis, Hunter corrected the natural geoid by the amounts of vertical displacement of the prolonged sea level necessitated by the assumed compensa tion of the topography. These corrections gave the “com pensated” geoid, which was found in fact to be little different from the natural geoid.* * Contour maps of the natural, “compensated,” and “isostatic” geoids were published by E. A. Glennie in vol. 5 of the Geodetic Reports of the Survey (1930). See also J. de G. Hunter, Mon. Notices Roy. Astron. Soc., Geophys. Supp. vol. 3, 1932, p. 42, where copies of the maps will be found. 232 Isostasy in Africa and Asia In the words of Hunter, the compensated geoid derives its form entirely from anomalies from Hayford’s hypo thetical density distribution. These anomalies may be dis tributed in an infinity of ways, and yet satisfy the facts of obser vation; but, with the simple assumptions that they are confined
F ig u re 47. Mass anomalies to match the Hayford anomalies of Figure 48. to the outer 70 miles of the earth and distributed uniformly along vertical lines, they have been calculated for India. Such density or mass anomalies are shown in Figure 47, where the anomalies are expressed as the mass having the normal density of surface rock (2.67) and distributed uni Isostasy in Africa and Asia 233 formly between sea level and the depth of 113.7 kilometers. The contour-interval is 1,000 feet of thickness for the mass before attenuation in this hypothetical way. A few maxi mum figures for the thickness are entered on the map.
Areas of positive anomalies are stippled. As usual, the anomalies were calculated on the basis of the International formula. From the mass anomalies the corresponding gravity anomalies were computed, and their range of values is indi cated by the contour lines of Figure 48. Here the contour 234 Isostasy in Africa and Asia interval is 20 milligals. Areas of positive anomaly are stippled. Hunter draws the conclusion: No one can say that Hayford compensation exists closely in con tinental India. The departures therefrom are far greater than the whole topography to be compensated in the greater part of the continent. Thus between the Ganges and the Himalaya is an area of negative anomaly, reaching as much as 6,700 feet and averaging 2,000 feet over an area of about 100,000 square miles. Subsequent paragraphs from Hunter’s paper are worth full quotation: The same failure of Hayford compensation of continental India is brought out when we seek the spheroid for India which fits (i) the Natural Geoid, (ii) the Compensated Geoid. The Natural Geoid is drawn with reference to an adopted spheroid; then we try to find a spheroid which fits more closely, and the measure of success is the sum of the squares of the ultimate separations. There is no prospect of the fit being perfect (sum of squares = 0), for the Earth is clearly neither smooth nor homogeneous. Now if we knew all about the form and density of the crust, which are the causes of the separation of the geoid from the spheroid, we could correct the geoid and reduce it to the spheroid from which it is distorted by the irregularities of form and density. If the process could be performed with per fection we should arrive at a perfect spheroid. If our attempt, though imperfect, is based on tolerably correct estimates of form and density, we shall arrive at a geoid—the Compensated Geoid we have called it—which will be an approximation to a spheroid and, as before, the measure of the success of the process is the sum of the squares of the ultimate separations between this geoid and the spheroid which fits it best. We should certainly expect to find the sum of the squares less than in the case of the Natural Geoid and its best-fitting spheroid. But we find in fact that the sum of the squares is considerably larger; that is to say, the Compensated Geoid is more irregular in form than the Natural Geoid. This clearly means that our estimates of the form and density of the crust were much astray; but of the form there is no doubt, it is well known. Therefore it is the estimate of the Isostasy in Africa and Asia 235 density that must be wrong, and this estimate was made on the Hayfordian hypothesis. When the same process is applied to the U. S. A. Geoids the result is markedly different. Here the Compensated Geoid gives a mean square residual which is only half of the Natural Geoid residual. It is clear that the hypothesis fits the one region but does not fit the other. Summarizing the result of his study of 18 Himalayan sta tion records, Hunter states: The Himalayan regions so far explored gravitationally exhibit gravity anomalies which are greatly reduced by the [Hayford] hypothesis, and indicate an average of 90 per cent, compensation. The average departure from complete Hayford compensation may be represented by an equivalent stratum 864 feet thick of ordinary surface rock (density 2.67) in excess. This is strong support for the hypothesis of mountain compensation, in accord ance with Pratt and Hayford. After once more emphasizing the value of Hayford’s method of discussing isostasy when the area of the United States is in question, Hunter writes: The fair conclusion seems to be that regions exist where the [Hayford] hypothesis closely resembles facts, but that regions also exist where precisely the reverse is the case. With less than 2 per cent, of the Earth’s surface gravitationally explored, it is useless to conjecture what proportion of the Earth accords with the hypothesis. There is no “principle of isostasy” in the sense that has often been implied, that is, of Hayford compensation; and it is misleading to use the term. We cannot presume that Hayford compensation has actuality in any region unless we find by measurement that it has. We certainly cannot compute the form of the geoid by assuming Hayford compensation, with any chance of success. On the other hand, we can use the concept of Hayford com pensation as an ideal standard, with reference to which gravity anomalies may be stated. In so doing we gain distinct computa tional advantages. Our anomalies will thereby very probably be freed of the disturbing effects of mountain ranges, etc., at great and medium distances; and even if on occasion this is not the 236 Isostasy in Africa and Asia case no harm is done. We shall know what our standard of reference is, as this is quite definitely defined, just as the size and location of our reference spheroid is defined. There may well be a “principle of isostasy” in the vaguer sense in which Dutton introduced the word isostasy. I think this could almost be expressed by changing the old expression, “water finds its own level”, into “the Earth’s crust finds its own level”. Surely it is merely a mechanical concept that the natural tend ency of the material of the crust is to adjust itself towards hydro- dynamical equilibrium, to which it may approximate more and more with lapse of time, but which it will never absolutely attain owing to the resistive strength of the materials of the crust. One would, indeed, be surprised if the ordinary laws of mechanics and of strength of materials were suspended in the Earth’s crust. But it is the artificial, though useful, and restricted sense of Hayford compensation, in which the compensating densities are for convenience arranged in vertical columns of uniform density anomaly, that the term “isostasy” has come to mean, and the “principle of isostasy” accordingly implies the existence of Hay- ford isostasy over the whole Earth—which is in opposition to the observed facts.9 However, there is some confusion here, for neither Hay- ford nor Bowie nor, apparently, any other worker in this field of thought has regarded the principle of isostasy as equivalent with Hayford’s assumed and admittedly unreal mode of compensation for topography. All authorities see that the compensation must be regional. G r a v it y A n o m a l ie s in I n d ia . S o much for the geoid and the testimony of the plumb line; what about the evi dence from measurements of the intensity of gravity? The warping of the geoid is a function of variations in the intensity of gravity along the geoidal level. It is therefore natural to expect that the gravity anomalies found in India should also compose into a Hidden Range belt of more posi tive anomaly and flanking belts, each of these two being characterized by anomalies smaller than those computed for the Hidden Range belt. This anticipation agrees with the Isostasy in Africa and Asia 237 facts, as shown by the latest (1938) map of Hayford anom alies. Here (Figure 49) the spheroid of reference is the 1930 International; the contour interval is 20 milligals; the posi tive areas are contoured and stippled; the negative areas are
F igure 49. Hayford anomalies in India, based on the International spheroid. contoured and left otherwise blank. The assumed depth of compensation is 113.7 kilometers. The most remarkable fact disclosed is the dominance of negative values among the anomalies. From the southern shore of Ceylon to the Himalayan front, a distance of 2,500 kilometers, there is a continuous negative zone, and even a 238 Isostasy in Africa and Asia large part of the Hidden Range belt is negative. The mean Hayford anomaly for all of the 306 peninsular stations listed in Heiskanen’s world Catalogue (1939), and situated south of the 28th parallel of latitude is —24.5 milligals (In ternational formula).* This mean is 19.5 milligals more negative than the mean for 448 United States stations, with reference to the same formula. (See Table 19.) The Indian mean would be near —17 milligals, if the depth of Hayford compensation were 80 kilometers instead of 113.7 kilometers. Incidentally, it is worth noting at once that the mean Indian anomaly would be much less negative if the individual anom alies were computed by Heiskanen’s 1938 triaxial formula for the earth’s figure. From the foregoing summary, it appears that the gravity anomalies, like the broad waves of the geoids, show peninsu lar India to be gravitationally in decided contrast with east ern North America, where isostasy has been canvassed with plumb line and pendulum. And we are to see that negative anomalies have been found in the wide Pamirs just north of India, and also across the Arabian Sea area to the west. Whether the conclusions apparently suggested by India re garding the distribution of mass, stress, and strength in the earth’s body can be reconciled with the conclusions reached in North America and Europe will be one of the themes of chapter 12. For the present, we continue the summary of the facts recorded by the officers of the Survey of India. From his early study of the deviations of the vertical from their theoretical directions, Everest deduced an ellipsoid of reference which seemed to match best the Indian data of his time. As the number of observations of deflection (espe cially by H. L. Crosthwait) and then of the intensity of grav ity (measured by H. J. Councilman and others) increased, * A map locating 506 Indian stations, and tables giving data for calculating corrections according to the Hayford type of isostatic reduction, are to be found in a Supplement to the Geodetic Report of the Survey of India for 1937 (volume issued in 1939). Isostasy in A frica and Asia 239 the Survey improved the formula, always aiming toward that ellipsoid which would give the most reliable basis for mapping the country. The most important of these indig enous formulas is that corresponding to the “Spheroid of
F igure 50. Hayford anomalies in India, based on the Helmert spheroid. India II,” which, as expressed in Table 2, contains the terms needed for comparison of values of gravity. This formula does not differ greatly from that of Helmert, which also ap pears in the Table. It is therefore instructive to glance at the Survey’s map of Hayford anomalies, based on the Hel mert 1901 spheroid and calculated from the data of 1936. 240 Isostasy in Africa and Asia Figure SO, a copy of the map, shows with stippling the large positive area over the Hidden Range, and the blank but contoured, negative areas to north and south.
Knowing that isostatic compensation can not be purely local, Glennie has computed the anomalies derived on the assumption that compensation entirely fails within a dis tance of 120,000 feet or 22.7 miles from each station. He based calculations on the Spheroid of India II. His 1937 map of the resulting anomalies is reproduced as Figure 51. Here the positive, Hidden Range belt is wider than the cor Isostasy in Africa and Asia 241 responding belt of Figure 50. It is also evident that an average of about + 10 milligals has been added to the anom alies throughout the peninsula—the joint effect of change of formula and introduction of the idea of failure of compensa tion to the extent postulated. For the broad inequalities in the field of gravity—inequali ties manifest in both geoidal map and anomaly map—Glen nie could find no adequate explanation in the horizontal variation of density among the surface rocks. In Profes sional Paper 27 of the Survey of India (1932) he developed the much more promising explanation which may be de scribed as the “crust-warping” hypothesis.10 It may be recalled that, according to the Hayford concep tion of isostasy, the part of the natural geoid covering a mountainous region of strong relief should not fit any sphe roid; normally it should have a low hump under a large group of such mountains as well as a slight hollow under each broad basin with surface well below the mean surface of a continent. But the demonstrated crests and troughs of the Indian geoids have no such relation to topography. The crest of the Hidden Range is located in an area of relatively low altitude. Similarly the geoidal troughs are not deter mined by the relief. These facts prompted Glennie, as offi cer of the Survey of India, to publish his new idea concerning the geoidal warps. He notes (p. 171 of his 1933 paper) that the Hidden Range arch in the compensated geoid runs across geological formations of every nature, from light recent alluvium to well-compacted ancient sediments, and across igneous rocks of various ages and types. . . . Pendulum results are similar; there is, in fact, a very marked correlation between geoidal heights and Hayford gravity anom alies. Here we have a direct negation of the claim made by isostasists, that exceptional Hayford anomalies will always be found to be due to purely local variations of density extending only over a small area. In India practically all the gravity anomalies seem 242 Isostasy in Africa and Asia to have no apparent relation to local conditions. Only one explanation seems possible—that is, that they are due to a very deep-seated gentle undulation of the lower crustal layers under lying all the superficial rocks; it is evidently a very uniform broad sweeping feature at a great depth, and must be uncompensated, since if it were compensated it would cause no anomaly at the surface. Like Heiskanen, Glennie has come to realize that help in the problem of the earth’s figure may well be sought among the discoveries of the seismologists. He decided to adopt Jeffreys’ picture of discontinuities separating the “lower crustal layers”: a “granitic” layer normally 10 kilometers (about 33,000 feet) thick, overlying in succession an “inter mediate” layer 20 kilometers (about 67,000 feet) thick and a “dunite” layer of indefinite thickness. This arrangement, along with assumed (uniform) densities for the layers, is shown in Figure 45, b, adapted from Glennie’s Figure 2 in Professional Paper 27. The drawing represents a section of the “crust” along the profile described in connection with Figure 45, a. For sim plicity in presenting the hypothesis of “undulation” or “crust-warping,” the rock surface of India is indicated as perfectly flat and at sea level. The normal positions of the discontinuities are given by the broken lines. The adjacent, continuous, gently curved lines represent to scale the warp ing of the layers by an amount sufficient to account for the Hidden Range. Over the southern trough no general cover of sediments is shown; hence the diagram implies that there also some of the original granitic layer has been removed by erosion. The stippled parts of the drawing represent excess of mass under the Hidden Range belt; the vertically lined parts represent deficiencies of mass. Because of the downward “warping or down-faulting of the earth’s crust,” the interface between granitic and inter mediate layers and the interface between intermediate and ISOSTASY IN AlRICA AND ASIA 243 dunite layers are locally depressed. It is assumed that the granitic and intermediate layers “go down without change of thickness. The dunite is considered plastic and is pushed aside; hence the down-warping is compensated by a rising up of the dunite layer in an adjacent area pushing up with it the upper layers.” By the shift of mass and corresponding change in the distribution of density, the depressed area must give negative anomalies and the raised areas positive anomalies. “Denudation of the raised area will expose the lower igneous rocks, or ancient sedimentary formations, and provide sediments to fill the depressed area.” The effect of the deformation on the value of gravity at the surface can be calculated when allowance is made for the difference of density at each of the two interfaces, namely, (2.85 - 2.67 = ) 0.18, and (3.3 - 2.85 = ) 0.45. Thus Glennie accounts for the Hidden Range by postulat ing an upwarp of the lithosphere, flanked on each side by a downwarp. All axes of the warps are assumed to be ap proximately parallel to the Himalayan front. The triple warping is thought to have taken place so long ago that above the belt of upwarping “denudation, deposition of sediments, and subsequent earth movements have removed all obvious surface indications of this warping.” By calcu lation Glennie found that a total maximum disleveling of the layers by an amount equal to about 9,000 feet would explain the anomalies of the Hidden Range.11 In order to see how local values of gravity would be affected by the warping and subsequent denudation, Glennie preferred to abandon Hayford’s assumption of perfectly local compensation and to assume no compensation out to a distance of 120,000 feet (22.7 miles) from each station, while outside that circle compensation is postulated. He wrote (p. 173 of his 1933 paper): Accepting the above seismological data, if the intermediate layer warps down below its normal level, it presses aside the lower 244 Isostasy in Africa and Asia layer, and above it the granitic layer warps down to the same extent. On the surface of the granitic layer deposition may obliterate all trace of the down-warp. The crust anomaly at the surface of the granitic layer will be that due to two cylinders, both with a radius of 22^ miles and a depth equal to the amount of the down-warp; the top of the first cylinder will be 10 kilometers (33,000 feet) below sea level, and its density will be the differ ence between the densities of the granitic and intermediate layers (2.67 to 2.85); the top of the second cylinder will be 30 kilometers (100,000 feet) below sea level, and its density will be the difference between the densities of the intermediate and lower layers (2.85 to 3.30). Taking as a numerical example a down-warp of 40,000 feet, the effect of the upper cylinder is — 54 milligals, and that of the lower cylinder is —67 milligals, hence the crust anomaly due to this down-warp is —121 milligals. This assumes that depo sition has filled the down-warp at the surface of the granitic layer with material of density 2.67. If this is not the case, due allow ance must be made in the same way. The effect of an up-warp is computed in a similar way. Glennie regards the old downwarp on the north as respon sible for the Tethyan sea of transgression, the Gangetic alluvial basin being a recently sedimented, partial relic of that much greater, ancient geosyncline. So far as this northern belt of negative anomaly is concerned, his hypothe sis has some warrant from the geology of the region. On the other hand, the area south of the Hidden Range lacks homologues of Tethyan sea and Gangetic geosyncline. Hence it appears that the crust-warping hypothesis, while well worthy of retention as a working tool, does not supply a completely satisfying theory of the situation in India. An alternative suggestion of a reason why the southern area has a depressed geoid, and dominantly negative anomaly, emerges from a principle to be symbolized under the name “coast effect.” (See p. 297.) The southern part of the peninsula has been subject to prolonged erosion. Because load has been removed to the ocean where it borders three sides of the area, the coast effect should here be more pro Isostasy in Africa and Asia 245 nounced than in cases, like that of California, where the ocean borders only one side of the denuded belt. It might be imagined that the disturbing mass, the Hidden Range, can be explained as a great total volume of dense igneous rock, injected high in the lithosphere, rock of the type represented by the Deccan trap. Glennie rejects this hypothesis because it lacks geological evidence, and he points out that the visible Deccan trap has little systematic influ ence on the gravity anomalies. Again with apparent justice, he regards as insufficient the reference of Oldham and Burrard of the negative anomalies over the Ganges alluvium to the low density of this sediment. Having satisfied himself that the major belts of anomaly are best understood by assuming the major warps of the lithosphere, Glennie then proceeds to use gravity anomalies for the location of minor crust-warps in the peninsula. As a preliminary he corrects the Hayford anomalies for the gravitational effects of the major warping, the anomalies being based on the preferred Spheroid of India II. He adds another correction to allow for failure of compensation out to distance of 120,000 feet from each station. The two cor rections together being applied, there remain final “crust- warp” anomalies, which were plotted on a map. From the plot the minor warps are deduced; on the map illustrating their axial trends is shown a great network or grid of minor crust-warps, distributed over the peninsula.* Glennie believes the hypothesis of crust-warping to be so well founded as to permit estimates of the thicknesses of the sediments still representing the old geosynclinal prisms of India. In illustration, some of his conclusions may be quoted (the 1933 paper, p. 174): (i) That the down-warp underlying the Cuddapah sediments extends at its deepest part to 14,000 feet below sea-level. * See chart IX in the Geodetic Report, Survey of India, for 1937 (1938). 246 Isostasy in Africa and Asia (ii) That the down-warp under the Vindhyan sediments goes 13,000 feet below sea-level. (iii) That the up-warp of the crust under Bombay amounts to 20,000 feet; if we allow a thickness of 13,000 feet of Deccan trap, the trap comes in contact with the intermediate layer, showing that one of the foci of effusion of Deccan trap is centred at Bombay. All the above numerical results are reasonably in accord with geological data. The fact that the Cuddapah and other ancient sediments in Peninsular India have been raised above sea-level without folding appears to indicate a general uplift uniformly affecting the whole of India; a general up-warp of this nature cannot be disclosed by gravity anomalies without data at sea outside the area of uplift. Glennie remarks that the crust-warping hypothesis in explanation of abnormalities in surface gravity had been in dependently developed by Vening Meinesz, and closes the 1932 paper with the following summary: A theory has been advanced that gravity anomalies are mainly due to density differences at the interfaces of the three crustal layers. The differences result from the down-warping (down- faulting through shear is not excluded) of the two upper layers. Accompanying the down-warp is an adjacent uprise of the crust. The theory has been tested numerically and appears to give satisfactory results where there is sufficient geological data to provide an independent check. As a result of the circumstance that positive anomalies are due to phenomena which are less deep-seated than those which cause negative anomalies, and that ordinary down-warpings tend to reach a stable position after reaching a uniform depth—(further warping if it occurs ending in failure of the crust, buckling of sedimentary rocks, etc.)—the illusion of compensation of topographical features down to a fixed level according to Pratt’s system of isostasy is obtained. Ranges which have been folded over ancient geosynclines have deep roots which more than compensate them; horst ranges and other “positive” areas of the crust are not due to decreases of density below but rather to the uprising of the denser layers of the crust. Isostasy in Africa and Asia 247 This theory appears to afford a plausible explanation for all the main tectonic features in and around India. Although isostasy as a fact is denied, as an illusion it persists; hence the presentation of gravity results in the form of Hayford anomalies still remains the best method for universal application as a first step towards the investigation of the structure of the Earth’s crust. (Professional Paper 27, pp. 27-8.)
OBSERVATIONS IN TURKESTAN Beyond the Karakoram chain of mountains and its west ern continuation, and only a few hundreds of kilometers north-northwest of the plains of peninsular India, is a large area where the Russian geodesists have measured gravity at 161 stations. The area lies between 37° and 45° of lati tude and between 65° and 78° of east longitude. It includes the Pamir mountains on the south and the Ferghana basin, already celebrated for its strongly negative anomalies, on the north. The basin is relatively flat, with elevations varying from 200 to 800 meters, but the middle and southern part of the region has mountain peaks, some of which reach heights of 5,000 meters or more. Fifty-four of the stations are in the Ferghana basin. V. Erola of Finland has computed for each observed value of gravity the Hayford isostatic reductions with 80, 113.7, and 160 kilometers as depths of compensation; Airy isostatic reductions with sea-level thickness of the sial assumed at 20, 40, 60, 80, and 100 kilometers; and the Vening Meinesz- regional reductions with depth of compensation at 0 to 25 kilometers and 25 kilometers.12 The mean of the free-air anomalies was found at —112 milligals, only six positive values being listed. The mean Bouguer anomaly (effect of the topography in zones A to O removed) is —240 milligals. The means of the isostatic anomalies came out as follows: We see that each mode of isostatic reduction gave a much smaller average deviation from the mean than the deviation 248 Isostasy in Africa and Asia in either of the corresponding free-air and Bouguer reduc tions. Applying the criterion that the best reduction should show anomaly least affected by height of station, Erola con cluded that 98 kilometers is here the most probable depth of Hayford compensation, and that the most probable sea-level thickness of the sial is about 35 kilometers. Omitting the stations in the Ferghana basin, this last thickness came out at approximately 20 kilometers. After calculating the sums
Hayford, D T in km : Airy, in km: Free-air Bouguer 80 113.7 160 20 40 60 80 100 Mean with regard to sign (milligals) -112 -240 -59 -57 -58 -57 -54 -52 -54 -57 Average deviation from mean, ± : 53 80 33 31 32 35 31 31 32 35 of the squares of the anomalies, the most probable mean thickness of the sial under the region as a whole is about 48 kilometers, but only about 28 kilometers if the stations in the Ferghana basin be excluded. In his summary, accompanied by an isanomaly map (Airy with D = 20 kilometers) and section showing the run of four kinds of anomaly, Erola states that, while isostatic reduction diminishes the anomalies, there remain —40 to —60 milli- gals, to be explained only by deficiency of mass under this extensive area. A more detailed report is in preparation. GRAVITY ANOMALIES IN JAPAN In 1927 Heiskanen published the Hayford (T = 113.7 kilometers) anomalies for 80 stations in Japan, basing calcu lations on his 1924 triaxial formula (see Table 2).13 With regard to sign the mean free-air anomaly was + 57 milligals, and the mean Hayford anomaly + 19 milligals. Referred Isostasy in Africa and Asia 249 to the 1930 International formula, these means are respec tively about + 65 and + 27 milligals. Forty stations on the largest island, Hondo, and south of Tokyo gave a mean Hayford anomaly of + 2 milligals (about + 10 milligals by the International formula). Twenty-six stations in Hondo, north of Tokyo, gave a mean of + 46 milligals (about + 54 milligals by the International formula). Fourteen stations on Hokkaido island showed a mean of + 27 milligals (about + 35 by the International formula). On each of the principal islands, Hondo and Hokkaido, the average became in general more and more positive in passing from west to east, that is, toward the Japan Deep under the open Pacific. To Heiskanen, this change is not accidental but most probably reflects a condition of regional compensation, the positive belt of eastern Japan being bal anced by a negative belt following the great Deep. As we shall see in the next chapter (Figure 66), Matuyama’s later measurements of gravity over the Deep have corroborated Heiskanen’s view. Thus, the main islands of Japan repre sent some excess of mass, the Deep an average deficiency of mass. Heiskanen believes that these abnormalities will ultimately be removed by a moderate warp-subsidence of Japan and moderate uprise of the floor of the Japan Deep. Such slow movements may be genetically connected with the pronounced volcanism of Japan. Twelve years later, Heiskanen listed in his world Cata logue the Hayford anomalies at 122 land stations in Japan, the anomalies being computed by the International formula. The values range from — 91 milligals to + 138 milligals, and their average is + 6 milligals. The 80 stations dis cussed in 1927 made the Hayford average + 25 milligals. The drop to + 6 milligals illustrates the common experience that increase of the number of stations occupied in a region reduces the mean isostatic anomaly. The mean Hayford anomaly for the 122 stations would be 250 Isostasy in Africa and Asia about + 11 milligals, if reduction were based on Heiskanen’s 1938 triaxial formula. . SOME LEADING RESULTS A word in review. This chapter has dealt with observa tions of gravity in three stable, “shield” areas of the litho sphere: East Africa, Siberia, and peninsular India. When reductions of gravity are referred to the International sphe roid and anomalies are averaged, the first two areas are seen to be in approximate isostasy. India shows a remarkable departure from this condition. When Heiskanen’s triaxial figure of the earth is adopted as the basis of reference, the mean anomalies in East Africa and Siberia are not changed enough to warrant doubt that both regions are essentially in balance, but peninsular India still shows the greatest waves of anomaly and apparently the greatest uncompen sated loads yet deduced in any continental sector. India, Turkestan, Japan, and the Rift belt of Africa all give out standing proofs of regionality as essential to the definition of isostasy, if this term is to mean anything useful. Among the conceivable causes for lack of balance, em phasis has been placed by Bullard and Glennie on horizontal compression of the lithosphere, leading in the Rift belt to fracture, underthrusting, and negative loads, and in India to fracture-warping and both positive and negative loads of wide span. Whether the uncompensated loads on the In dian sector can be stably borne by a lithosphere, resting on a perfectly weak asthenosphere—a condition implied in ideal isostasy—is one of the most vital questions emerging from the study of continental gravity. That difficult subject of inquiry will be debated in chapter 12. There it will be argued that, if the asthenosphere is essentially liquid, the lithosphere under India must have average strength com parable with that of granite at low temperature. Isostasy in Africa and Asia 251
References 1. E. Kohlschiitter, Nachr. Gesell. Wissen. Gottingen, 1911, p. 1. 2. W. Stackler, Inaug. Dissertation, Berlin, 1926; E. Krenkel, “Die Bruchzonen Ostafrikas," Berlin, 1922. 3. A. Born, “Isostasie und Schweremessung," Berlin, 1923, p. 36. 4. E. C. Bullard, Phil. Trans. Roy. Soc. London, vol. 235a, 1936, p. 445. 5. See W. Heiskanen’s Catalogue (Annates Acad. Sci. Fen- nicae, ser. A, vol. 51, No. 10, 1939), p. 100. 6. See R. D. Oldham, Memoirs Geol. Survey of India, vol. 42, 1917, p. 127. 7. E. A. Glennie, Survey of India, Prof. Paper No. 27, 1932, Fig. 1. 8. G. Bomford, Survey of India, Geodetic Report for 1934, plate 21. 9. J. de G. Hunter, Mon. Not. Roy. Astr. Soc., Geophys. Supp., vol. 3, 1932, pp. 46 and 49-51. 10. See also E. A. Glennie, Mon. Not. Roy. Astr. Soc., Geophys. Supp., vol. 3, 1933, p. 170. 11. See E. A. Glennie, Survey of India, Prof. Paper 27, 1932, especially pp. 11-2. 12. V. Erola, Annales Acad. Sci. Fennicae, ser. A, vol. 51, No. 12, 1938. 13. W. Heiskanen, Zeit.f. Geophysik, vol. 3, 1927, p. 213. 9 TESTING ISOSTASY AT SEA
INTRODUCTION Since geodetic triangulation is impossible over oceans, which cover seventy per cent of the globe, the isostatic hy pothesis can not there be examined by the plumb-line method. Fortunately, measurement of the intensity of gravity at sea has become so accurate as to permit the alter native method. The bearing of the resulting gravitational data on the problem of terrestrial strength is less obscured by two conditions that do affect the study of values found on the lands. In the first place, the measuring apparatus in the deep sea is several thousands of meters from any rock, so that the differential attraction of local masses of rock with abnormal density and near the surface of the lithosphere complicates the situation much less than in the case of a land station. Secondly, as Vening Meinesz points out, the interpretation of gravity values over the oceans, outside the coastal shelves, is comparatively little troubled by the exist ence of local anomalies of mass which have been developed by erosion and sedimentation. This ninth chapter is a summary of the amazing progress made in the gravimetry of the oceans, especially within the last ten years. After brief reference to the Hansen-Schiotz results of the “Fram” expedition and to the work of Hecker, cruising in three oceans, the summary will continue with a more detailed account of the peerless researches of Vening Meinesz, whose methods have made also possible the valu- 252 Testing Isostasy at Sea 253 able studies of gravity at sea by Cassinis, Matuyama, Soro kin, and a number of experts associated with the United States Coast and Geodetic Survey and the United States Navy. We shall review the general results bearing on the degrees of isostasy represented in the great ocean basins, several mediterranean seas, the topographically complex regions of East Indies and West Indies, the ocean Deeps, and the inshore belts of the open ocean along the visible limits of continents, volcanic islands, and major deltas. OBSERVATIONS OF HANSEN, SCHIOTZ, AND HECKER The first notable attempt to measure gravity over the deep sea was made by Scott Hansen in the steamship “Fram” of the Nansen polar expedition. An appropriate pendulum was, at considerable intervals of time, swung on the polar ice, which gripped fast to the ship while slowly drifting across the Arctic basin. The values of gravity thus found were later reduced by Schiotz. Fourteen of these sea-level values gave a mean anomaly of + 15 milligals, when computed from the Helmert 1884 formula (see Table 2), the corresponding mean being — 13 milligals when computed from the 1930 Inter national formula.1 Although the conditions of the field work were not particularly good, the result was of the kind expected if the Arctic sector of the earth is in close isostatic balance with the continental, Pacific, and Atlantic sectors. Between 1903 and 1910, Hecker was able to publish three reports on values of gravity on the high seas as well as on seas of the mediterranean type. He used an instrumental method which had been proposed by Guillaume.2 The height of the mercury column in a barometer is independent of the intensity of gravity at the point of observation. At the same point the boiling-temperature of water gives the absolute pressure of the air, which does depend on the in tensity of gravity. If, then, the height of the mercury col umn and the boiling-point of water can be measured with 254 Testing Isostasy at Sea
F igure 52. The Tonga Deep. Numbers show depths of water in thousands of meters. Testing Isostasy at Sea 255 sufficient accuracy, the intensity of gravity at any station can be calculated.* Hecker developed a photographic ap paratus for recording the height of a mercury column, with error not exceeding 0.01 millimeter. The boiling-point of water can be fixed with an error no greater than 0.002°C. Hecker found how to correct for the motion of the ship dur ing the readings. The total irreducible error in the measure ment of gravity had a range of about 30 milligals. The mean free-air anomalies, referred to the 1930 Inter national formula for the figure of the earth, were found to be in milligals: For the Atlantic Ocean, — 7; for the Indian Ocean, + 13; and for the Pacific Ocean, — 13. Helmert discussed the results and concluded that “gravity over the ocean has a range of the same order as that found over the continents; hence we have now confirmed, by Hecker’s in vestigations, the essential truth of the doctrine of isostasy.”3 Hecker traveled also over the Black Sea, where gravity was discovered to be in general not far from normal. Of special interest are the results of his traverse across the Tonga Deep of the southwest Pacific (Figure 52). Over the Deep itself the free-air anomalies, referred to the Interna tional formula, were consistently and strongly negative, with limit, as measured, at — 287 milligals (corresponding to about — 194 milligals, isostatic). Immediately to the east ward of the Deep, he recorded positive free-air anomalies up to +80 milligals; and on the west, over the submerged Tonga Plateau, they were again positive with maximum of about + 250 milligals (not very different from what the matching isostatic anomalies would have). Between Sydney, Aus tralia, and Auckland, New Zealand, the free-air anomalies averaged more than + 200 milligals. All these numbers are so large that it seems right to expect future work with more * The mode of calculation is described by W. Heiskanen in the “Handbuch der Geophysik” (ed. by B. Gutenberg), Berlin, vol. 1, 1934, p. 764. 256 T esting Isostasy at Sea reliable apparatus to prove great deviations from normal gravity in the two sections described. MEASUREMENT OF GRAVITY AT SEA, BY VENING MEINESZ Just such improvement in instrumental equipment has been made by F. A. Vening Meinesz, and there must be few geologists who have not already meditated on the wealth of new facts already reported after his various journeys in sub marines. Vening Meinesz had set himself to devising a pendulum apparatus which would give reliable results on the unstable ground of the Netherlands. Success in that enterprise led to the perfecting of an instrument for use in a submarine when sunk to a moderate depth, below the levels of strong wave-action. By repeated and thorough trials it was found that this instrument is capable of measuring grav ity with a standard error no greater than 3 milligals—the normal error allowed in the case of the best pendulum ap paratus for use on the land. For so complete a conquest over the difficulty of designing adequate equipment, for his prolonged, self-sacrificing work among the dangers to life on an ocean-going submarine, and for his unquenchable ambition to allow for every conceivable error in measurement and in reductions of his observations, geophysicists and geologists can not express too much ad miration. Twenty years ago it would have seemed hardly conceivable that such accuracy of measurement of gravity at sea could be obtained, and that one man could, within a few years, measure gravity all around the world and prove that gravity in every part of our planet is amenable to meas urement. In 1923, Vening Meinesz made his first important cruise— from Holland to Java by way of the Suez Canal. With the experience gained, the apparatus was modified and tested in a voyage from Holland to Port Said (1925). The following Testing Isostasy at Sea 257 year a third journey was made from a home port to Java by way of the Azores, Canary Islands, Panama, Mazatlan, San Francisco, Honolulu, Guam, Caroline Islands, Manila, and Banda of the Molucca group of islands. Depths of water were determined by echo-sounding. In 1927 some weeks were spent on measurements of gravity in the Indian Ocean, with special interest in the Java Deep. During the autumn of 1928, Vening Meinesz transferred his apparatus to a sub marine of the United States Navy and, with the collabora tion of F. E. Wright and E. B. Collins, made a round-trip traverse from Washington past Key West to Galveston, the Mississippi delta, Cuba, the Bartlett Deep, Saint Thomas, the Nares Deep, and the Caribbean Sea. In February and March, 1932, a second study of the West Indian region in a submarine of the United States Navy was made, T. T. Brown, E. B. Collins, and H. H. Hess co-operating. This cruise began at Guantanamo, Cuba, crossed the Bartlett Deep, rounded the western end of Cuba, and completed sev eral sections of an extensive region including the Bahama Islands. July and August of the same year saw Vening Meinesz again at work in a submarine of the Netherlands Navy, the object being to investigate especially those parts of the North Atlantic which are seismically active. From Holland the course led to the English Channel, the Azores and the mid-Atlantic Swell, Madeira, and back to Holland. In 1932, Vening Meinesz published a first volume, bearing essential data from the earlier traverses, and in 1934 a second volume, giving the free-air, Bouguer, Hayford-isostatic, “Heiskanen” (Airy)-isostatic, and “Regional” anomalies for all 486 stations occupied before the year 1933. This second report is by long odds the most important of the publications yet made on the subject of gravity at sea.4 In 1937, B. C. Browne indicated the need of systematically correcting the values of gravity at sea for an error due to dis turbances caused by the movement of the submarine. This 258 Testing Isostasy at Sea matter was at once investigated by Vening Meinesz, who has recently published a list of corrections for the “Browne term,” to be applied to the values of 183 stations. The maximum correction there entered is —44 milligals; the minimum, — 1 milligal. The correction could not be made at the first 32 stations occupied, for a technical reason. In the case of each of the remaining 271 stations, the error proved to be one milligal or less and thus practically negli gible. 6 At sea each of the listed free-air anomalies equals the dif ference between the sea-level value of gravity at the station corresponding to the adopted spheroid of reference and the observed gravity, after the latter has been corrected. The correction required is double: for the depth to which the sub marine was sunk during the measurement, and for the attrac tion of the layer of water between the surface of the sea and the level at which measurement was made. As with all the other kinds of anomaly, the computation was based on the 1930 International spheroid. The Bouguer anomalies reported by Vening Meinesz are only partly analogous with those usually given in the reduc tion for land stations. (See p. 116.) In order to remove the effect of the (submarine) topography, the theoretical gravity at a sea station must be increased by the attraction of a mass with density of 1.64, equal to the mean density of the upper sial, 2.67, minus the density of sea water, 1.03. The hypothetical mass was assumed to be circular, centering at the station, and having a radius of 166 kilometers, the outer limit of the Hayford-Bowie ring 0. The listed Hayford anomalies were computed on the usual assumption of local compensation, and the depth of com pensation was held at 113.7 kilometers. The corresponding Airy (named “Heiskanen” by Vening Meinesz) anomalies were calculated on the assumptions: (1) that the densities of “crust” (sial) and “substratum” (sima) Testing Isostasy at Sea 259 are respectively 2.67 and 3.27; (2) that the sea-level thick ness of the sial is 40 kilometers; and (3) that the compensa tion, here too, is purely local. Anomalies of the new type, called “regional” may be re garded as modified-Airy. Now topography in positive re lief is regarded as a load which bends down the lithosphere, without breaking it, until the upward pressure of the asthen- osphere balances the mean downward pressure of the topog raphy. Thus (p. 35 of the 1934 report): the compensation is regional; in a horizontal sense it is distributed proportional to the vertical displacement of the crust under the effect of the loading of the crust by the topography. In a verti cal sense the distribution depends on the assumptions about the density in the crust; if this is assumed to be the same over the whole thickness of the crust, the compensation is concentrated at the lower boundary of the crust. For the crust’s thickness, a value of 25 kilometers has been taken. This seems a low figure compared with the figure of 96 kilometers of Bowie, but firstly the compensation is supposed to be concentrated entirely or for the greatest part at the lower boundary of the crust and so we must compare with the depth of the center of gravity of the com pensation according to Bowie, i.e. with 48 kilometers, and, sec ondly, the compensation is regional and it is easy to see that this diminishes the depth that best satisfies the field of attraction at the surface. Each regional anomaly was computed by allowing for cor responding change in the values of Hayford compensation from zone to zone around the station. Vening Meinesz noted the “indirect-isostatic or Bowie” reduction (see p. 126), but decided that its application would make no great change in the conclusions that may be drawn about the meaning of the other anomalies, the modifi cation of these being practically negligible. Mean Gravity Anomalies over the open Ocean. It will be long before the full significance of the 486 measure ments of gravity can be told, but some important correla 260 Testing Isostasy at Sea tions are already apparent. To illustrate, let us begin with a comparison of the means of the anomalies respectively found in the three oceans. For this purpose we shall use the data from stations over deep water but well removed from the gravitationally ab normal Deeps and also from the disturbing influence of the lands. The stations chosen were occupied during the Hol- land-Suez-Java voyage of 1923 and during the Holland-
T able 34 MEAN ANOMALIES OVER THE DEEP OCEANS ' (milligals; 1930 International spheroid)
Mean Depth Frce-air Modified Hayford Airy Regional (meters) Bouguer (“Heiskanen") P acific San Francisco to Ha waii (10 stations) 4,925 + i +278 +4.8 +0.5 +5 Hawaii to Guam (14 stations) 5,010 +2.5 +288 + 5 0.0 +4.5 Atlantic Traverse of 1926 (12 stations) 5,193 - 4 +292 + 10 + 5 +9 I ndian Ocean T raverse of 1923 (6 stations) 3,878 -2 7 + 189 -2 1 -2 6 -25 P acific + Atlantic (36 stations) — + 1 — + 7 + 2 +6 P acific + Atlantic + I ndian (40 stations) — - 1 — + 5 ' 0 + 1.5
Panama-Hawaii-Java voyage of 1926. Under each station the water exceeded 3,000 meters in depth. The anomalies, corrected for the Browne term, were reduced to means with regard to sign. The results are shown in Table 34, which, be it noted, refers merely to a series of stations distributed along a line of circumnavigation that was confined to a zone between 10° and 40° of north latitude. The reference Testing Isostasy at Sea 261 spheroid was the 1930 International, and the depth of Hay- ford compensation was held at 113.7 kilometers.* The map of Figure 53 gives the values of the Hayford anomalies computed for the stations along the line of the
Figure'53. Hayford anomalies across the Atlantic Ocean (milligals). transatlantic voyage. Figure 54 contains similar data for the Pacific, between San Francisco and Guam. * Vening Meinesz has recently published a table showing the mean Hayford, Airy, and regional isostatic anomalies (International formula) along 34 traverses across the open ocean. One of the most striking features of the table is the positive sign of the Hayford anomalies (+27 and +24 milligals) and regional anomalies (+16 and +20 milligals) in two traverses, between Cape Town and the south point of Madagascar and between Mauritius and a station at 30° south latitude and 72° east longitude. Both stretches are in the broad belt where we might have expected negative anomalies, if Heiskanen’s 1938 triaxial formula represents the true figure of the earth. This lack of agreement may mean a special excess of mass under the western part of the Indian Ocean. On the other hand, the case illustrates the uncertainty about the true figure of the earth that must remain until many more measurements of gravity are made in the southern hemisphere. See the paper of F. A. Vening Meinesz in the “Advanced Report of the Commission on Continental and Oceanic Structure,” presented to the General Assembly of the International Union of Geodesy and Geophysics, Washington, September, 1939 (p. 41). 262 Testing Isostasy at Sea The means of the free-air and isostatic anomalies are so small as to prove how remarkably well the smoothed geoid fits the International formula. Evidently the oceanic sec tors of the globe are, in general, close to perfect isostatic equi librium; in the words of Vening Meinesz himself, there is “decided confirmation of the principle of isostasy.” We note, too, that the Airy hypothesis is particularly successful in reducing the anomalies over the Pacific and Atlantic oceans. However, the open-ocean stations within the northern part of the Indian Ocean give negative anomalies, both indi-
Figure 54. Hayford anomalies across the Pacific Ocean (milligals). vidually and on the average. These stations are only six in number, but their data are the more significant because the hundreds of stations on adjacent peninsular India are also ruled by negative anomaly. This negative character of the whole Arabian Sea-India region tends to corroborate Heis- kanen’s 1938 triaxial formula for the figure of the earth. (See Table 2, p. 31.) The short axis of the implied elliptical equator emerges at 65° east longitude, and thus the corre sponding meridian crosses the middle part of the region; hence the triaxial formula requires negative anomalies when reductions are based on the International formula. Testing Isostasy at Sea 263 The Heiskanen formula has the major axis of the equa torial ellipse emerge at 25° west longitude and at 155° east longitude. On both sides of each of the meridians passing through those points, the formula demands positive anom alies when computed by the International formula. As a matter of fact, in both cases broad meridional belts of one- sign, positive anomaly are indicated by the Vening Meinesz results. Table 35 gives average anomalies for the belts (again after corrections for the Browne term).
T able 35 POSITIVE ANOMALIES IN MERIDIONAL BELTS (means with regard to sign; milligals; International formula)
Free-air Hayford Airy Regional 76 stations, between 0° and 50° of west longitude (eastern Atlantic) + 15 +31 + 25 +20 172 stations, between 120° and 180° of east longitude (western Pacific) + 11 +20 + 15 + 19
It may also be noted that the 281 stations of the East Indies (an area measuring 2,000 by 4,500 kilometers and extending between the meridians of 100° and 135° of east longitude) give respective means for the free-air, Hayford, and Airy anomalies at + 17, + 15, and + 18 milligals. We have already found one-sign, negative anomaly in the broad meridional belt covering land along the western mar gin of North America and thus traversed by the meridian where the short axis of Heiskanen’s equatorial ellipse emerges on the side of the earth opposite to the Arabian Sea. It is indeed clear that one of the chief reasons why Heis kanen developed his triaxial formula was his proper weight ing of the results of Vening Meinesz. The geophysical and geological importance of this particular spheroid was re ferred to in the last chapter and later will be considered again. 264 Testing Isostasy at Sea Gravity Anomalies over Mediterranean Seas. An other leading discovery of Vening Meinesz is the rule that the smaller, more or less inclosed seas that were traversed during his cruises are characterized by positive mean anom aly of large magnitude. Table 36 gives the means for the Banda Sea, an East Indian type of these deep seas of trans-
F iguke 55. Hayford anomalies in the Tyrrhenian Sea (contour-interval, 50 milligals). gression; for the Gulf of Mexico; and for the Red Sea. Also entered are the means for the Tyrrhenian Sea, bounded by Italy, Corsica, Sardinia, and Sicily (Cassinis expeditions); and the mean free-air anomaly resulting from Sorokin’s ob servations on the Black Sea.6 In addition, the means from all of Cassinis’ 98 observations in the Mediterranean (tabu Testing Isostasy at Sea 265 lated in Heiskanen’s world Catalogue, p. 128) may be stated. Here, with average depth of water at 1,505 meters, the mean free-air anomaly comes out at + 4.5 milligals; the mean Hayford anomaly (T = 96 kilometers) at + 35 milligals. Figure 55 shows contours for the Hayford anomalies in
Figure 56. Hayford anomalies in the Gulf of Mexico (milligals). the Tyrrhenian Sea (T = 96 kilometers; International for mula). Figure 56 gives the Hayford anomalies (T = 96 T able 36 MEAN ANOMALIES OVER MEDITERRANEAN BASINS (milligals; International formula)
Number Mean Hayford of depth Free-air (r = 113.7 Airy Regional stations (meters) km) Banda Sea 26 3,612 +24 +55 +50 +65 Gulf of Mexico 13 2,485 + 1 +23 — — Red Sea 4 812 + 6 +57 +50 +55 Tyrrhenian Sea 48 1,890 + 13 ca. +27 — — Black Sea 59 1,650 -31 — — — 266 Testing Isostasy at Sea kilometers) in the Gulf of Mexico. If T be taken at 113.7 kilometers, about 3 milligals should be subtracted from each value. The mean Hayford anomaly for all 17 stations in the Gulf is +16 milligals. The deep sea-basins most thoroughly investigated are those of the East Indies. They are largely concentrated in the eastern half of this enormous region. The marine part of the western half, between Sumatra-Java and Borneo- Celebes, is identical with the Sunda Sea of MolengraafPs nomenclature (the Java Sea of Vening Meinesz). Here, for a distance of 2,000 kilometers, the water keeps a nearly con stant depth approaching 50 meters, and the mean Hayford, Airy, and Regional anomalies are respectively +24, +28, and +32 milligals; the variations from the means are small. After remarking that the western area is “stable,” Vening Meinesz writes: “The eastern part of the archipelago has an entirely different character. From a tectonic standpoint it is unstable and the submarine topography is extremely irreg ular.” Here are two principal basins, distinguished as the Celebes Sea and the Banda Sea. The former contains six stations, giving mean anomalies of +89, +71, and +78 milligals. The anomalies remain positive, not only over the relatively flat floors of the basins, but also up to the shores of the surrounding islands. In general, the anomalies are the more positive as the depth of water increases. Vening Meinesz proceeds: The correlation of deep basins with excesses of gravity has also been found in another tectonically active area, viz., in the West Indies; the gravity expeditions of the U. S. Navy have shown strong positive anomalies in the Gulf of Mexico [see Figure 56 here] and in the sea west of Cuba, and here also the transition from the positive values towards normal gravity on the borders of the basins has in several places been found to be a sudden one. This correlation may be considered as an unexpected result. When expressing it in terms of isostasy, it means that the basins Testing Isostasy at Sea 267 are strongly over-compensated. So, when we assume that there is a tendency towards the readjustment of the equilibrium, we should have to expect that they must still tend to become deeper. (1934 report, pp. 114-5.) An adequate reason for the correlation is given as a princi pal conclusion of Umbgrove, Kuenen, and Waterschoot van der Gracht, who have studied the geology of East and West Indies, namely, that these basins are recent formations that have come into being by a subsidence of areas that were originally continental or epi continental. . . . Admitting the truth of this hypothesis we have to look for an explanation that can account for the positive anomalies as well as for the sinking. (1934 report, p. 135.) After a brief discussion of alternatives, Vening Meinesz wrote: So we are led to the only explanation that the writer has been able to find for accounting for this combination of subsidence and positive anomalies, the development of a downward con vection-current in the substratum. [Such a current must] bring about excesses of mass, which give rise to positive anomalies at the Earth’s surface. At the same time the surface of the sub stratum above the sinking current must be lower than that above the [convcctively associated] current and so the subsidence of the area agrees likewise with this supposition. . . . The question arises whether perhaps these convection-currents might be responsible for the compression of the crust that is at the base of the whole tectonic phenomenon. Thanks to the investigation of Umbgrove this question can receive an answer and this answer is in the negative. He proves clearly that the sinking must have occurred after the great folding process of the mobile belt in the Miocene. . . . Knowing that the development of the convection-currents has occurred after the period of the principal folding, we are led to the supposition of a causal relation of these two phenomena. A possible explanation of such a relation can readily be given. It has already been mentioned that the formation of the root of crustal material at the lower boundary of the crust [see the description of the “negative strip” to be given later in the present 268 Testing Isostasy at Sea book] must alter the temperature conditions, because it brings about a concentration of material that is more radioactive. So the temperature of the vicinity must be heated up. It seems reasonable to suppose that this will lead to the development of convection-currents in the substratum which will rise below the mobile belt and sink down in the adjoining areas. In this way the subsidence of these last areas could be explained at the same time as the rising of the belt. Before the current develops, the heating of the zone in the belt must already cause some rising of the surface of this area, but once the current sets in, this rising must further increase because the rising current brings warmer
layers of the substratum in the place of cooler layers and so the temperature of the whole column increases. In the same way the sinking current in the adjoining area brings cooler layers in the place of warmer layers and the temperature of the column diminishes. So in these areas the surface must undergo a sink ing although there was no cooling of the substratum here at the start. . . . The increasing temperature difference between the rising and sinking columns must further accelerate the current and so the whole process has an unstable character, i. e. in the beginning it increases more or less proportionally to its own intensity. After some time it reaches a stationary situation, which depends on the values of the viscosity, the coefficient of thermal expan sion, the thermal diffusibility, the density and the original tem perature gradient of the substratum and of the dimensions of Testing Isostasy at Sea 269 the phenomenon. Until that stationary situation is reached, the rising of the belt and the sinking of the adjoining basins will con tinue. The whole process will strongly lag behind the period of folding in the tectonic belt which is its cause. This is in har mony with the facts in the East Indies; the subsidence of the basins must have occurred in a later period than the folding. (1934 report, p. 136.) A difficulty faced by this hypothesis involving convection will be described in chapter 12.
F igu re 58. Anomalies over the eastern part of the East Indian “strip.”
St r ip o f N e g a t iv e A n o m a l y , E a st I n d ie s . The most celebrated discovery of Vening Meinesz regarding the com plexities of the earth’s field of gravity is that suggested by the generic name “negative strip.” This startling phenom enon was first reported in the East Indies, and has become even more intriguing since another great example was found in the West Indian region. The East Indian strip has been studied in the greater de tail, and a descriptive sketch of the famed example has log 270 Testing Isostasy at Sea ical precedence. Here the strip, “dominating the whole field,” consists of “a narrow belt of strong negative anom alies, running through the archipelago, and bordered on both sides by fields of positive anomalies.” (See the map of Figure 57 and the continuing map of Figure 58.) The strip, stippled in the maps, keeps a fairly constant width of about 100 kilometers. It crosses the islands west of Sumatra, fol lows a swell-like rise of the floor of the Indian Ocean south of Java; follows the west-east arc containing Rotti, Timor, and Letti islands; then bends sharply to follow the semi circular course of the island arc including Tanimber, Kei, and Ceram islands. Interrupted by a 150-kilometer stretch between Ceram and Obi Island, the strip, turning northward, becomes again highly conspicuous between Halmaheira Island and Celebes Island. Opposite Obi Island an east- west branch crosses Banggai Island and possibly curves back to follow the broad southeastern peninsula of Celebes. The colored map of anomalies in volume 2 of “Gravity at Sea” indicates a northerly termination of the strip at a point about 200 kilometers north of Talaud Island, but Vening Meinesz believes that after such local interruption the strip continues to and beyond the Mindanao Deep off the Philip pines. Figure 59, copied from van Bemmelen’s 1935 map in the Geologische Rundschau, also illustrates the systematic dis tribution of the isostatic anomalies. Figure 60 gives four of the twenty-one gravity profiles (Hayford anomalies, dotted lines), drawn across the strip and published in the original memoir. All the profiles show the same feature, a strong subsidence of the three anomaly-curves over the belt and positive values to both sides. The gradients of the anomalies are steep to both sides of the belt; in many cases it is even astonishingly so. Tables 37, 38, and 39 list actual figures for the anomalies at F igu re 59. Van Bemmelen’s map showing regional-isostatic anomalies in the East Indies, 272 Testing Isostasy at Sea a few of the cross sections (anomalies referred to the Inter national formula). In further comment on his results, Vening Meinesz writes: The profiles clearly show that the negative anomalies are not brought about by a wrong assumption about the distribution of the compensating masses. The three anomaly-curves are so similar that we need not doubt that the differences which dif-
JAVA JAVA DEEP (7140 m) TIMOR ------1 ------+1004 mg a I s — —L' ------— ------— - 1—
NDIAN OC
— — — - 100 mgals A B
57S 0 m 8600 m 5570 m BANDA CELEBES T A L A U D PACIFIC 1 C E L E B E S SOELA SEA SEA ,D 5 \ OC i i i 4 + ?00 igals l
------— - 1 0 0 mgols
- 200 mgaIs C D F igu re 60. Hayford anomalies across the East Indian “strip.” ferent methods of reduction may cause, are far inferior to the principal feature. This is likewise demonstrated by the Bouguer anomalies. They show that the strip of negative anomalies is already there before applying any compensation at all. . . . The profiles, as well as the bathymetric map, which contains a representation of the topography of the sea-bottom, show that the belt of negative anomalies is generally coinciding with a row of islands or a submarine ridge. This is rather unexpected, because it precludes the idea that the gravity defect could be caused by an uncompensated topographic mass-effect. The situ ation of the belt is strongly against this supposition because it is nearly everywhere beside the deep troughs that occur in the archipelago. Testing Isostasy at Sea 27 3
T able 37 GRAVITY ANOMALIES ACROSS THE NEGATIVE STRIP: N.N.W. TO S.S.E., FROM CELEBES SEA THROUGH NORTHEAST CELEBES AND SOELA ISLAND TO BANDA SEA (milligals; corrected for “Browne term”)
Distance No. of apart Depth Free-air Modified Hayford Airy Regional station (km) (meters) Bouguer 340 5,178 +31 +343 + 83 + 55 + 5 8 100 339 5,570 -2 1 +307 + 7 4 + 4 6 + 73 100 338 1,830 + 75 + 188 + 67 + 6 7 + 72 110 333 1,245 +117 + 190 + 9 4 + 9 4 + 95 45 332 3,600 -1 0 7 + 111 -2 7 -3 8 0 80 324 2,468 -1 8 3 -3 7 -1 6 8 -1 7 4 -1 6 4 150 279 895 +228 +285 + 159 + 156 + 135 85 280 4,800 + 5 8 +357 + 134 + 106 + 129 80 282 5,170 + 4 +296 + 9 6 + 8 0 + 95 120 284 4,130 + 15 +246 + 5 0 + 38 + 39
T able 38 GRAVITY ANOMALIES ACROSS THE NEGATIVE STRIP: EAST-WEST SECTION THROUGH TALAUD ISLANDS (milligals; corrected for Browne term)
No. of Distance Depth station apart (km) (meters) Free-air Hayford Airy Regional 150 5,140 + 8 0 + 136 + 108 + 119 225 270 870 +201 + 125 + 136 + 117 70 269 3,320 + 12 + 4 2 + 5 4 + 6 0 70 268 980 - 3 9 -1 3 2 -1 1 8 -1 5 2 125 267 7,780 -7 8 + 67 + 2 5 + 7 8 25 266 5,790 + 2 4 + 99 + 6 6 + 9 4 100 265 5,390 + 2 9 + 65 + 42 + 4 6 274 Testing Isostasy at Sea
T able 39 GRAVIMETRIC SECTIONS OF THE JAVA DEEP Sections 16 to 13 in order from west to east; stations listed in order from north (toward islands) to south (toward Indian Ocean); anomalies in milligals; corrected for “Browne term”
Distance Depth Station No. apart (km) (meters) Free-air Hayford Airy Regional Section 16 182 230 + 153 + 76 +82 +81 95 183 2,210 -80 -125 -130 -140 100 184 6,610 -73 + 29 -11 +31 100 185 4,780 + 79 + 74 + 73 +52 165 186 5,280 +25 +41 +30 +38 Section 15 181 130 + 110 +55 +65 +59 80 180 3,020 -19 + 16 + 13 +30 65 179 1,320 -20 -103 -105 -127 90 178 7,080 -165 -35 -68 -22 80 177 5,040 +30 +59 +46 +46 130 176 4,390 +32 +35 +31 +31 Section 14 169 150 + 7 -17 - 5 -12 80 170 270 + 133 +64 +66 +61 95 171 3,950 -84 -33 -47 -28 80 172 2,680 -5 0 -79 -96 -114 70 173 6,680 -153 -27 -66 -13 75 174 4,280 + 28 +36 +26 +24 125 175 4,180 +22 +29 + 15 +14 Section 13 297 3,420 -100 - 3 - 6 +21 65 Testing Isostasy at Sea 275
T able 39 (Continued)
Distance Depth Station No. apart (km) (meters) Free-air Hayford Airy Regional 166 0 + 119 + 72 +91 +62 40 198 0 + 88 +23 + 17 + 17 25 197 500 + 63 + 17 + 2 6 + 19 65 199 2,298 - 7 + 1 + 3 + 8 90 200 4,234 -1 4 7 -1 0 6 -1 1 7 -1 1 5 65 201 4,600 -4 0 - 3 -2 4 -2 4 105 202 5,400 + 23 + 63 + 3 8 +41 80 203 5,500 + 2 0 + 53 + 33 + 29
(See Figure 60.) Nevertheless, Vening Meinesz notes that strip and topographic trough (Deep) “are everywhere par allel to each other and close together. An explanation of the belt will, therefore, have to account for this relation.” (1934 report, p. 111.) As a rule, the transverse curves of anomaly are nearly sym metrical, though decided asymmetry characterizes the pro files west of Sumatra and at the Mindanao Deep (Figure 64). The negative strip is explained by its discoverer on the basis of his already well-known “buckling hypothesis.” He emphasizes the deviation of the strip from the axes of the associated belts of specially deep water. On the other hand, the strip generally coincides with island rows or submarine ridges and so this excludes its being caused by topographic mass-effects that are uncompensated. . . . It appears also unlikely that it is caused by recent movements of the Earth’s surface which, when brought about by tectonic forces, might have caused disturbances that are not yet com pensated. This would mean that we should have to assume a sinking of the surface in the belt and this is in contradiction with 276 Testing Isostasy at Sea the unmistakable evidence of rising that is found on many islands of the belt. In general it does not appear probable that the belt would be in a state of down-warping. The steepness of the gradients, from the negative values within the strip toward the positive values alongside the strip, make it probable that the cause of the negative anom aly is situated near the earth’s surface. “A depth of some forty kilometers seems about the maximum that can be ad mitted.” The strip must be underlain by a great amount of light mass in the upper layers of the Earth. When assuming a defect of density of 0.6, we find that a cross- section is needed of more than a thousand square kilometers. What can be the cause of this surprising feature and where do we have to localize it? Only considerations from other sides can guide us in trying to find an answer to these questions.” (1934 report, pp. 117-8.) S. W. Visser had mapped the epicentra of the earthquakes affecting the East Indies between 1909 and 1926, and Vening Meinesz points out (1934 report, p. 112) that nearly all of the epicentra fall in the negative strip. He adds: We must assume that the mass-defect is narrowly related to the tectonic activity in the archipelago. Now all the geological evi dence points towards great lateral compression in the Earth’s crust in this area and this conclusion is likewise borne out by the submarine topography of the archipelago as it is clearly demon strated by Kuenen.7 Under the lateral compression (which still exists) the crust gives way, with local thrusting and thickening of the rela tively light sial and with concomitant sinking of the under lying sima, pressed down and aside by the local, added weight. Thus a sialic root is developed, and this downward protuberance of the sial “causes a great mass-defect corre sponding to the strong negative anomalies.” Any upward bulge of the sial at the surface is T esting Isostasy at Sea 277 by far insufficient to compensate by its attraction the defect of gravity corresponding to the root. . . . This hypothesis thus gives a natural explanation of the fact that the belt is usually coinciding with a ridge and not with a trough. It likewise explains that the phenomenon is accompanied by heavy earth quakes. . . . The question may be considered why the downward bulge of the crust develops so much quicker than the upward bulge, although it might be thought that the substratum must exert a resistance, which is not met with by the upward protuberance. The resistance, however, of the substratum is probably viscous and so it must be small when the speed of the downward move ment is small. Gravity, on the contrary, must favour the forma tion of the downward bulge, because this bulge has to be pushed downwards against a density difference of about 0.6, while an outward bulge, that has to be pushed upwards, has a density of about 2.7. (1934 report, pp. 118-9.) The way in which the root was made is a vital problem. Vening Meinesz quite agrees with Smoluchowski that unas sisted horizontal compression could not change a homo geneous, dead-level lithosphere into a warped, wavy litho sphere ; the layer would fail by simple fracture or by localized crushing.8 However, on the assumption, justified by seis- mological and other evidence, that the lithosphere is divided into sub-layers of varying strength, he believes it possible that waves will develop of a length of one or two hundred kilometers, which originally will be symmetrical with regard to the normal position of the crust, i.e. the outward waves have the same height above it as the downward waves are below it. When the downward waves get below sea-level, they become deeper. Gradually erosion and sedimentation will alter the phenomenon and the downward waves will tend to subside more and more. At a certain stage, the strength of the crust will be exceeded and disrupture sets in in the downward waves, which will buckle inwards. A root begins to develop. The surface layer of the crust will no doubt undergo strong crushing in the central buckling zone and it can easily be under stood that, at a certain stage of the phenomenon, it will begin 278 Testing Isostasy at Sea to bulge outwards in irregular folds, which will cover the down ward buckling of the main crust-layer. Thus a ridge will develop. In case this superficial layer is thinner or perhaps even lacking at one side of the ridge, we may expect that at that side the downward movement is not quite hidden and that a trough will reveal it. In the archipelago, many instances of this are found; several troughs exist beside the buckling zone and always at the deep sea side of the zone. Striking examples are found south of Java, near the Tanimber Islands and near the Talaud Islands. Figure 61 is a diagram illustrating this hypothesis of origin. The sima and lower, thicker part of the sial are represented by line-shading; the upper sub-layer of the sial by the stipple
F igu re 61. Illustrating the origin of the East Indian “strip,” according to Vening Meinesz. pattern. The assumed horizontal shear of sial over sima is from left to right. It should be noted that the density at tributed by Vening Meinesz to the sima is that of crystalline peridotite, and yet, according to his convection hypothesis, this material has vanishingly small strength. Until new experimental or other evidence is found in support, it may well be doubted that the combination of such high density with such low strength can characterize any known type of rock. When in a later stage of the phenomenon the compressive forces are again decreasing, the crust will get more liberty to resettle locally in isostatic equilibrium. The zone of strong nega tive anomalies must have a strong tendency to rise but in the present stage the lateral pressure in the crust is apparently too Testing Isostasy at Sea 279 great to allow of such a readjustment independently of the neighbouring areas. It may, however, be expected that this will come to pass in a later stage when the compression has diminished. So, in the long run, the rising of the ridge will probably reestablish the isostatic equilibrium and the whole structure will then have reached the last stage of the folded mountain-range, in equilibrium over its compensating root of crustal material at the lower boundary of the crust. Such a stage, for instance, is realized in the Alps and in other folded mountain ranges. (1934 report, pp. 119-20.) From Figure 61 and from the last of the quoted paragraphs it appears that Vening Meinesz regards the negative anomaly of the strip as only in part the gravitational effect of the root; it is also due to a moderate downward buckling of the litho sphere. By this elastic depression the lithosphere is being temporarily held down, below the level of equilibrium. The correlative, expected super-elevation of the lithosphere on each side of the strip means excess mass under these low arches and explains the peripheral belts of positive anomaly.* Geological tests of the hypothesis seem to support it. (1) Kuenen has shown that the development of the troughs close to the strip must be genetically connected with the folding and thrusting within the strip itself. (2) As already stated in principle, Umbgrove proved that no islands in the archipelago, save those in the belt, show great folding or overthrusting, while those in the belt that have been investigated—and this is the great majority—show clear evidence of it. So it can be considered to be proven that this belt has been subject to strong folding and overthrusting while no other part of the archipelago has undergone crustal shorten ing of a comparable amount during the Tertiary. * Vening Meinesz and also Hess give diagrammatic sections through the earth’s crust where the mountain roots (strips) are fully developed. In both cases the crust below the geosynclinal sediments is represented as having been down-buckled into a tight, closed fold by pure bending, without fracture. That the segment of the crust here involved could yield in this way is highly doubtful. Much more probable is a process of throughgoing fracture (thrust-faulting), followed by down- bending of the broken crust. 280 Testing Isostasy at Sea The suggested explanation of the strip invites two impor tant deductions. The first conclusion is that we have obviously to do with a border effect of the Asiatic continent. It does not appear risky to express the view that it forms part, on one side, of the geosyn clinal belt that continues from the Himalaya towards the south east and, on the other side, of the belt of arcuate island ridges that borders the Asiatic continent on the east side; it seems to form the connection between those two geosynclinal belts. So the Himalayan gcosyncline does not appear to continue towards New Guinea, as it has often been supposed, but towards Japan. In the second place, it is worth while to remark that the anomalies are just as strong in the part of the belt that borders on the Indian ocean than [sic] in the part bordering on the Australian continent. This appears to indicate that the resis tance offered by the ocean-floor of the Indian Ocean is not inferior to that offered by the Australian continent. It is not necessary to point out the importance of this conclusion for our general views about continents and oceans. It seems to be a decided contradiction to Wegener’s theory of continental drift: we could not well imagine such a migration through the ocean- floor when this part of the crust can so strongly resist pressure.
The approximate symmetry of the transverse gravity profiles indicates approximate symmetry for the root also; after buckling inwards, the sial was “thrust more or less vertically downwards.” Vening Meinesz estimated the dimensions of the root at the profile from Java through Christmas Island of the Indian Ocean, and found the area of a vertical cross section of the root to be about 1,200 square kilometers. From this result we may conclude that the crustal shortening of a crust of a thickness of 25 kilometers would be about 50 kilometers because the product of both dimensions must correspond to this cross- section. This value for the crustal shortening cannot be con sidered as more than an indication of the order of magnitude, Testing Isostasy at Sea 281 because the above value for the thickness of the crust is uncer tain. Still it gives some idea about the movements that have actually taken place. Where, as west of Sumatra, the gravity profiles are strongly asymmetric, it seems best to assume the downward displacement of a slice of the lithosphere which was horizon tally sheared over the rest of the lithosphere. Vening Meinesz concludes that the compression is not acting in all directions in the crust but only in one which probably is best assumed to be about S.S.E. This direction makes only a slight angle with the direc tion of the belt west of Sumatra and so the movement in this area would indeed be chiefly a sliding of one part along the other with only a small component towards each other. . . . Near Strait Soenda the direction of the belt changes and the angle enclosed with the supposed direction of the force increases. The relative movement of the two crustal parts would thus get here a much stronger component at right angles to the belt, which means a greater shortening of the crust. This is in harmony with the altered character of the gravity profiles, which in profile No. 16 suddenly assumes the symmetrical type cor responding to such a shortening. (1934 report, pp. 121-2.) Having reached a conclusion as to the sense of relative motion of the lithospheric segments, Vening Meinesz pro ceeds to apply a third geological test to his buckling hypothe sis. The many volcanoes of the region are characteristically located on the concave sides of the strip, regarded in ground plan. “They mostly occur in rows parallel to the belt and at a distance of about 100-200 kilometers.” The explana tion reads as follows: If the crust moves towards a straight part of the belt, we must expect strong stresses in the sense of the movement but only sec ondary stresses in a sense parallel to the belt. When, however, the crust is moving from the inside of a curved part of the belt towards the belt, the stresses in the sense of the movement will be about the same, but parallel to the belt it is likely that tensile 282 Testing Isostasy at Sea stresses will develop, because we must expect that the dimen sions parallel to the belt must tend to increase when the crust moves towards the buckling zone. It appears admissible that these tensile stresses will facilitate the formation of volcanoes because of the corresponding relief of pressure, although the area as a whole must be under strong compression. (1934 report, p. 125.) This statement recalls an earlier suggestion by E. Horn con cerning the relation of volcanism to mountain arcs in gen eral.9 Vening Meinesz then applies his buckling hypothesis to other regions of Tertiary orogeny. In three ways he ac counts for the fact that the older mountain ranges have been uplifted long after the respective paroxysms of folding. First, such vertical movement took place when the horizontal compression, which had been holding down the root region below the level of isostatic equilibrium, was relaxed. Sec ond, after the development of the root, the rocks depressed along the disturbed belt began to be slowly heated from be low and expanded, with consequent rise of the rocky surface. Third, the concentration of the more radioactive sial in the root developed there special heating and additional expan sion in the vertical direction. This, too, is a leisurely proc ess, meaning long delay in the uplift. This conclusion agrees in a remarkable way with the facts that have been discovered by the geomorphologists. It has been gen erally recognized that the morphological evidence in the existing mountain ranges compels us to admit these ranges to have only reached their great elevation after the folding had already sub sided. This seems a support of the buckling hypothesis as it proves that the period of greatest horizontal shortening of the crust has not been characterized by high surface features. So, as the crustal material must have disappeared somewhere, the only remaining possibility is that it disappeared downwards in the substratum. This is exactly what the gravity results in the East Indies show to be the case and what has been formulated in the buckling hypothesis. Testing Isostasy at Sea 283 When the root becomes plastic, another consequence must be that under the influence of gravity it will, at least partially, flow away along the lower boundary of the crust. So we must expect that the root will become broader and that, therefore, the gravity field in older mountain ranges will no longer show the same narrow belt of strong negative anomalies but a broader zone of less intense deviations. This is undoubtedly the case. When we examine the case of the Alps, for instance, which have been so thoroughly investigated in every sense and where the gravity field is known in detail thanks to the survey of Niethammer, we see no evidence of a narrow strip of negative anomalies. Appar ently isostasy has been reestablished in this area and the actual root of the mountain-system seems to have about the same width as the system itself. When, however, we examine the isostatic anomalies in the Alps more accurately, we see that this is not quite the case. In the central part small negative anom alies are found and in the adjoining zones small positive anom alies, and so this seems to point to a root that is still slightly nar rower than the mountain-system itself. . . . [This conclusion] follows likewise from the results of the investigations of Eero Salonen, who applied the Heiskanen system of isostatic reduction with different assumptions for the thickness of the crust. All the curves which he obtains for the attraction of his different compensation assumptions show a broader curve in the central part and a smaller difference between the anomalies in the cen tral part and in the adjoining zones than the observed gravity shows. (1934 report, p. 127; see p. 202 of the present book.) Further support for the hypothesis is found in the fact of curvature for the world’s orogenic belts when viewed in ground plan. There is offered an explanation for the diving of the lower layer of the lithosphere under the nappes of the central Alps of Europe; also explanation for the bilateral thrusting, outward on each side of the axis of the Alpine chain—as described by Born, Stille, Kober, and others.
The reason why the East Indian strip is still strongly nega tive, in spite of the length of time elapsed since the Miocene 284 Testing Isostasy at Sea paroxysm, is given by Umbgrove, who postulates renewed thickening of the root during a period that began during Plio-Pleistocene time and is not ended yet, as suggested by the seismic activity of the strip.
Finally, Vening Meinesz briefly discusses the cause of the strip orogeny, stating in conclusion: We have to do here with a movement towards the S.S.E. of this part of the Asiatic continent with regard to the floor of the Indian Ocean and Australia. As far as the gravity results allow a con clusion, it seems as if these last crustal parts have no relative movement; the absence of great folding along the west-coast of Australia points to the same result. The floor of the neighbour ing part of the Pacific appears to have a movement relative to Asia as well as to Australia. . . . The fact that the relative movements in the Archipelago point to forces in one or two directions only, makes it difficult to explain them by the contraction hypothesis. If that were the cause of the phenomenon, it seems likely that the compression ought to come from all sides, unless at least great irregularities in cooling, in thermic properties or in clastic properties would occur, but even in this last case the above distribution of the stress seems difficult to explain. The writer is tempted to look for the cause, or at least one of the causes of the relative movements in con vection-currents in the substratum. (1934 report, p. 133.) The buckling hypothesis is evidently a special form of Airy’s root idea, which, however, Airy did not associate with any theory of origin for the roots. For clearness it should be noted that Vening Meinesz rec ognizes another kind of negative strip, namely, one deter mined not by increase of thickness of a sialic root by buck ling, but by mere down-bending of the lithosphere without drastic buckling, the warp being accompanied by horizontal outflow of the asthenospheric material below the flexed zone. A strip of the second kind is, thus, interpreted as due to T esting Isostasy at Sea 285 crust-warping, like that postulated by Glennie. (See p. 243.) Valuable supplements to the account of the strips and of the East Indian field of gravity in general are three chapters included in vol. 2 of “Gravity Expeditions at Sea” : chapter VI, on the relations between gravimetry and geology, by J. H. F. Umbgrove; chapter VII, on theories of the structural evolution, also by Umbgrove; and chapter VIII, on the rela tion between the submarine topography and the field of gravity, by P. H. Kuenen. After Vening Meinesz had evolved his theory of the strip, Heiskanen generalized the relations of root to mountain- structure, recognizing three cases. First, we have moun tains with roots, typified by the Alps and the Rocky Moun tains; second, mountainous masses without roots, like the Harz Mountains; third, roots without visible mountains, illustrated by long stretches of the East Indian strip, as well as the West Indian strip, soon to be described.10
NEGATIVE STRIP OF THE WEST INDIES Gravity over the ocean in the West Indian region has been measured at about 150 stations, two thirds of which were occupied by Vening Meinesz during his voyages of 1926, 1928, and 1932; the other stations were occupied by A. J. Hoskinson, M. Ewing, and H. H. Hess during a winter (1936-7) cruise in the United States submarine “Barra cuda.”11 The mean Hayford anomaly (International for mula), computed from all the results, is about —12 milligals, but, owing to some overemphasis on the values found over the negative strip of the region, it seems that the region as a whole is in almost perfect isostasy. It may be noted also that it is crossed by the meridian which is exactly half-way between the meridians where the longer and shorter axes of the equatorial ellipse of Heiskanen’s 1938 triaxial spheroid emerge. Over the Caribbean Sea, twelve stations west of the 75th T si g estin I sostasy
at S ea
I'iG uric 62. Map of the axis of the West Indian “strip” (after Hess). Depths in fathoms. Testing Isostasy at Sea 287 meridian gave an average Hayford anomaly of +23 milli- gals. Thirty-five stations on the same sea, but east of the 75th meridian, gave an average of nearly +4 milligals. As a whole, then, the Caribbean seems to represent another “mediterranean” basin with some excess of gravity and mass. The whole great area is bounded on the north and east by the negative strip, the axis of which is indicated by the heavy, broken line in Figure 62. The strip, rivaling that of the East Indies in its interest for dynamical and structural
F igu re 63. Hayford-anomaly profiles across the West Indian “strip” (Bowie formula; milligals). All values would become about 9 milligals more negative if computed by the International formula (T = 113.7 kilometers). The broken line represents the 4,000-fathom isobath. > 288 Testing Isostasy at Sea geologists, has been traced, with no apparent interruption, for at least 2,800 kilometers, and, according to Hess, it may approach 5,000 kilometers in length.12 Three cross sections of the strip are represented in Figure 63, where SL has the double duty of indicating sea level and also the line of zero anomaly. The section C-C shows that the negative strip practically coincides with the floor of the Brownson Deep, but section A-A shows no direct relation between strip and submarine topography, just as Vening Meinesz found along parts of the East Indian strip. See also Table 42, where it is seen that the size of the isostatic anomaly does not vary directly with depth of water. The essential features are remarkably like those of the East Indian strip, including: (1) great length; (2) relatively small width—100-50 kilometers; (3) negative free-air anomalies with maximum numerical value of about 300 milligals; (4) negative isostatic anomalies reaching at least — 175 mil ligals; (5) strong curvature in ground-plan, as illustrated in Figure 62; (6) close association with Deeps, elongated in the same sense; (7) a tendency to run along one flank of the neighboring Deep, rather than to follow its axis; (8) a strong tendency toward symmetry for the transverse gravity profiles, whether these profiles correspond to free-air or isostatic anomalies; (9) origination in Tertiary orogeny, though at a date which Hess fixes at the end of the middle Eocene and thus considerably earlier than the main (Miocene) folding along the East Indian strip;1 :l (10) recent volcanism at many points along a line parallel to, and just inside the curve of, the strip; (11) seismicity of the region as a whole, though, as compared with the East Indian case, weaker and less concentrated along the negative strip; (12) presence of pre-Tertiary, terrigenous sediments in the islands of the strip, indicating that formerly the sial adjacent to Testing Isostasy at Sea 289 these sedimented areas had nearly the normal thickness charac terizing the continents—a condition that would account for long- continued dry land in the region. As yet, however, there appears to have come no field evidence that the Caribbean area was in a state of emergence after the strip originated. Herein there may be an important failure of analogy with the situation in the East Indies, where, as already noted, the interior basins are thought to have been developed long after the Miocene folding; (13) one of the causes for the negative anomaly along the strip being the enforced depression of the belt below the level of isostatic equilibrium (Hess, in accord with Vening Meinesz). That even the disturbed West Indian region is, as a whole, close to isostatic equilibrium is apparent from Bowie’s dis cussion of the relevant 258 anomalies available in 1934.* He divided this vast area into “squares,” each equal to about 70,000 square miles, and determined, after proper weighting, the average Bouguer anomaly and average isostatic anomaly in each “square.” After weighting, there remained 208 in dividual anomalies to be averaged. Table 40 gives the result. T able 40 MEAN ANOMALIES IN WEST INDIAN “SQUARES’1 (milligals; International formula) )er of square Bouguer anomaly Isostatic anomaly i + 192 +41 2 +24 - 5 3 +90 -17 4 +317 +24 5 +395 +28 6 +355 +22 7 + 124 -45 8 +61 - 5 9 +36 -13 10 + 128 +8 11 +263 +46 12 + 154 + 12 13 + 189 + 19 14 +79 -47 15 + 160 -41 Mean + 171 +2 * See W. Bowie, Bull. Geol. Soc. America, vol. 46, 1935, p. 869, where neither figure of reference nor depth of compensation is given. 290 T esting Isostasy at Sea Heiskanen agrees with Bowie’s conclusion that the region is nearly in balance, as is shown in the following quotation: The isostatic anomalies are therefore in every square much smaller—from 1.7 to 16.1 times smaller—than the Bouguer anomalies. If the isostatic assumption explains the gravity anomalies in many mountains almost completely, it is also in this disturbed region a very good approximation,14 ANOMALIES OVER OCEAN DEEPS FACING MOUNTAIN-ARCS Deep sialic roots account well for a large part of the anom aly in each negative strip, but another part must be due to the negative attraction of the topographic troughs alongside the respective roots. Still clearer is the fact that the root idea can not supply a logical explanation for the imposing foredeeps of the open ocean, where there is nothing to corre spond with an “outward bulge” of the sial, matching a much more pronounced “downward protuberance” of the rela tively light rock. Yet the Deeps have large negative anom alies, both free-air and isostatic. Some examples have already been encountered where the
MINDANAO DEEP
F ig u re 64. Gravity profile across the Mindanao Deep. axes of the two great strips coincide more or less perfectly with the axes of foredeeps. The Mindanao Deep (Figure Testing Isostasy at Sea 291 64) and the Nero Deep (Figure 65) illustrate the case. Other negative belts are situated over foredeeps which seem to have no close association with sialic roots.
F igu re 65. Gravity profile across the Nero Deep.
In spite of Hecker’s instrumental errors, his study of the Tongan region has given a classic example of a long, open geosyncline bearing large negative anomalies and flanked by at least one positive belt. (See p. 255.) With a total am plitude of more than 500 milligals (free-air) and more than 400 milligals (isostatic), this huge wave of the lithosphere is evidently far from isostatic equilibrium, except in the sense that compensation for the topography is broadly regional. It is not surprising that the Tongan area is the scene of per haps the most intense seismicity of modern recording. The measurements of Vening Meinesz over the Yap Deep, carrying at least 7,600 meters of water (Table 41), and over 292 T esting Isostasy at Sea
F ig u re 66. Map of free-air anomalies over the Japan Deep. Testing Isostasy at Sea 293 the Nero (Mariana) Deep with 10,000 meters of water (Fig ure 65), seem to prove that the localized depression of the Pacific floor is alone practically sufficient to account for the negative anomalies there discovered. On the other hand, Matuyama’s report on the Japan (Nip pon, Tuscarora) Deep suggests nearer analogy with East Indian cases, where the gravity trough does not so closely coincide with the topographic trough, but lies a little to one side.15 In Figure 66, the depth of water off Japan (shaded) is indicated with unbroken isobathic lines, the Roman nu merals giving depths in thousands of meters. The area of (free-air) anomaly is stippled. The contour interval for both negative and positive anomalies is 100 milligals. It will be observed that locally the negative belt diverges from the Deep, and that the positive belt also has no rigorously held relation to the topography of the sea floor. Other instances are represented at the four sections across the Java Deep, Figure 60. Table 42 gives the anomalies along a cross-profile of the West Indian Bartlett Deep.
T able 41 GRAVITY ANOMALIES ALONG EAST-WEST SECTION ACROSS THE YAP DEEP (milligals; corrected for Browne term; International formula)
Hayford Airy No. of Distance Depth Frcc-air {T = 113.7 {D = 40 Regional station apart (km) (meters) km) km) 137 2,350 +77 +20 +39 + 19 130 140 4,510 0 +30 +20 +43 20 138 7,690 -154 -2 3 -3 9 + 7 30 139 0 +288 + 76 +63 +45 240 141 4,780 + 10 + 34 +30 +46 294 Testing Isostasy at Sea
T able 42 GRAVITY ANOMALIES ACROSS THE BARTLETT DEEP (milligals; International Formula)
Depth (meters) Hayford No. of station Free-air (T - 113.7 km) North of Deep: 23 0 +93 + 6 26 1,730 +35 +45 Above Deep: 22 5,250 -203 -6 7 25 6,900 -198 + 10 South of Deep: 24 4,630 -9 0 + 19 21 2,900 -4 2 -1 4 44 3,180 -2 8 +23
GRAVITY PROFILES OFF SHORES Vening Meinesz has listed the regional, Hayford, and Airy anomalies found in profiles run from continental shores to the deep ocean, that is, transversely to continental shelves. His latest table gives the record for 29 profiles. In seven cases the regional anomalies show algebraic decrease as the depth of water increases; in five cases the Hayford anomalies vary in the same sense. The Airy anomalies were computed for only 14 profiles; here only one gave decrease of anomaly with increase of depth of water. The great majority of the profiles showed variation in the opposite sense. The aver age algebraic increases of the regional, Hayford, and Airy anomalies in passing from shallowest to deepest water are 34, 45, and 32 milligals respectively.16 Table 43 gives eleven typical examples of the larger group of profile records. Vening Meinesz points out that, since the algebraic in crease of isostatic anomaly is in question, the increase has nothing to do with the coast-effect on the free-air anomaly, demonstrated by Helmert and his colleagues (see p. 54). The actual change of isostatic anomaly along the typical profile is, in fact, just the opposite of what might have been Testing Isostasy at Sea 295 reasonably expected from the nature of the inshore topog raphy under the sea. T able 43 GRAVITY-PROFILES FROM CONTINENTAL SHELF TO OCEAN (milligals; International formula)
Isostatic anomaly Depth of Profile water Regional Hayford Airy (meters) (Vening (T = 113.7 (D = 40 Meinesz) km) km) Atlantic ocean End of English Channel 170 - 4 - 4 +6 4,220 + 16 +45 +23 West of Lisbon 10 -26 -25 -10 5,053 +24 +31 0 West Africa, near Cisneros 75 -65 -67 -58 3,105 -2 +5 + 1 North America, near Cape Henry 60 (?) -29 -28 -23 3,990 + 1 +22 + 10 East of Pernambuco 10 -42 -51 — 4,950 -24 - 9 — Pacific ocean Mexico, near Tejupan Point 710 -15 -10 -17 5,030 +30 + 17 - 6 West of San Francisco 10 -5 -10 -5 680 -7 0 -64 -60 4,140 +5 +9 - 8 Indian ocean West of south point of Mada- gascar 150 -32 -37 — 4,305 +46 +56 — Southeast of Socotra 80 -73 -61 -51 4,210 - 9 -3 - 8 South of Point de Galle, Ceylon 65 -62 -52 -50 3,920 -3 -19 -27 Freemantle, western Australia 10 -100 -118 ------4,830 + 17 +24 — In vol. 2 of his “Gravity Expeditions at Sea,” Vening Meinesz briefly discussed the cause of such “discontinuity” in the gravity profiles off coasts. He there wrote (p. 206): It appears as if there are at least two effects that can bring about this . . . increase of the anomalies at about the same place where the depth increases. In the first place the slope may have been 296 Testing Isostasy at Sea caused by a subsidence brought about by a descending con vection-current in the substratum; this current must at the same time give rise to positive anomalies and so the correlation of the two features is automatically brought about. In the second place we can imagine that the steep shelf has originated by a tectonic folding phenomenon; several instances are known where a con tinent has thus been added to by an orogenic process along its borders. In this case we may expect positive anomalies beside the shelf and negative anomalies below it. . . . So, according to these considerations, the feature would not everywhere have the same cause. Vening Meinesz seems to have later abandoned both hypotheses in favor of others, which, however, he offers as merely working tools. These newer ideas are expressed in the 1939 paper (p. 43): In two ways we may perhaps find an explanation of this fea ture. First an error in the distribution of the compensation adopted by the system of isostatic reduction of Hayford may be expected to have a large effect near the continental edge where the change of topography is sudden and intense. If, for example, the assumption of Airy is true as a general idea, that is to say, if the crust is floating on a sub-crustal layer of greater density, we ought not to be surprised if the edge of the continental block for the part that is submerged in the deeper layer has not the shape that corresponds to the surface-topography according to the idea of local compensation. Some systematic difference from this distribution may explain the above systematic feature in the gravity-anomalies. The results found by Ewing on the shelf east of Virginia by means of his remarkable seismic work—since repeated by Bullard over a profile at the end of the Channel—suggest another possible explanation. Ewing, as well as Bullard, found the older layers dipping away when proceeding seaward over the shelf and this indicates the shelf as consisting for a great part of loose sediments. Near the edge of the sediments the thickness of this layer appears to be several thousands of meters. Now the topographic and isostatic reduction of the gravity-results has been based on a specific density of the crustal formation of 2.67, which doubtless is far too high for those loose sediments; their density may be 0.5 Testing Isostasy at Sea 297 to 1.0 less and perhaps the error is even greater. So with regard to the supposed situation there is a deficiency of mass in the shelf and a corresponding excess of mass in the actual isostatic com pensation and both masses taper off, more or less, on the conti nental side while they end rather abruptly near the continental slope. A simple computation shows that such a mass-distribu tion must bring about an anomaly-curve showing a fairly steep increase of the anomalies, algebraically speaking, over or near the continental slope, and this is exactly what has been found. The size of this anomaly-jump is of the right order of magnitude. So the results of Ewing and Bullard may give a satisfactory ex planation for this feature of the gravity-anomalies. A continuation of Ewing’s researches on other continental shelves may show whether these results are generally valid; this certainly would not be surprising. However, until we have ob tained more data, we can not yet know whether we may try this line of explanation everywhere. Of course, it may be possible that on some coasts other effects give a similar effect. Besides the above possibility of a wrong assumption of the isostatic com pensation, we may think of special causes working near coasts where mountain-forming parallel to the coast-line has been going on, for example, the west coast of Central and North America, where we may expect zones of transition from negative to positive anomalies parallel to the tectonic axis.
ANOMALY + ANOMALY - !< Inshore Belt >!< Offshore Belt >! ^CONTINENT . _ __ j , OCEAN ______S I A L ~~ ——- f j ~~ ------SIMA Lithosphere I ------j------*------A-B e f o r e ! Er o s io n . i i
ANOMALY - ANOMALY + In isostasy | Defect of mass^ ] Excess of mass j In isostasy :3n"^'-'~^-irT~ | ______j______Sea/evet ~~load T T T T — — -______1 1 1 * i i i B - A f t e r E r o s io n
F igure 67. One cause for the algebraic increase of gravity anomaly in passage from a continental shore to deep water. 298 Testing Isostasy at Sea In these quotations Vening Meinesz has made it clear that a multiplicity of causes is highly probable. Among them is one recently suggested by the present writer. Prolonged denudation transfers load from the marginal belt of a conti nent or large island to the corresponding offshore belt of de position. Because the lithosphere has considerable strength, the dry-land belt can not rise, and the offshore belt can not sink, to the extent needed to give complete, local isostasy. The result is an algebraic increase of the anomalies in passing from an inland point outward to the deep sea. (See Figure 67.) Such a disturbance of the field of gravity by secular erosion may be conveniently called a “coast-effect.”17
GRAVITY ANOMALIES IN THE VICINITY OF VOLCANIC ISLANDS The observations of Vening Meinesz are significant with respect to still another geological problem: how is the lofty deep-sea volcano, emergent or not, held up? Have the vol canic islands roots that compensate largely for these great masses, projecting thousands of meters above the general sea-floor?
Figure 68. Gravity anomalies in a profile across Oahu Island. Testing Isostasy at Sea 299 We note first the data secured near Oahu Island of the Hawaiian group. Figure 68, a section about 1,300 kilo meters in length, gives them in a form readily grasped; nu merical values can be read from Table 44.
T able 44 GRAVITY ANOMALIES IN AN EAST-NORTHEAST SECTION ACROSS SOUTHERN OAHU (corrected for Browne term; milligals; International formula)
Distance Number apart Depth Free-air Modified Hayford Airy Regional of station (km) (meters) Bouguer 109 4,590 + 4 1 + 2 9 9 + 3 0 + 3 2 + 3 2 200 110 4,510 + 3 + 255 - 6 - 9 - 6 75 111 5,430 - 9 6 + 2 1 6 - 3 8 - 4 8 - 1 3 150 112 510 + 165 + 139 + 2 9 + 5 9 + 2 3 35 113 0 (Honolulu) + 2 1 3 + 163 + 5 0 + 7 5 + 3 5 100 114 4,290 - 1 8 + 217 + 2 + 3 + 2 6 225 115 4,590 + 14 + 2 6 8 + 17 + 14 + 2 2
Some comments may be quoted (1934 report, p. 106): To the north-east the islands are bordered by a broad trough which is not deep; the greatest depth in this profile is only 5,529 meters, while the slightly elevated ridge to the north-east of the trough shows a depth of about 4,400 meters. The gravity-profile shows remarkable differences among the three curves of anom alies. While the curve of the Heiskanen [Airy] anomalies has deviations of — 50 milligals over the trough and +75 milligals over the island-ridge, the curve of the regional anomalies only shows — 13 milligals over the trough and +37 milligals over the ridge, i.e. its fluctuations are less than half of those of the first curve. In fact these fluctuations are remarkably small for an area where the topography shows great irregularities. Another 300 Testing Isostasy at Sea assumption for the data of the regional reduction may perhaps even further reduce them. . . . We may conclude that the assumptions on which this regional reduction is founded are in good agreement with the gravity anomalies and so it appears as if gravity can be explained for a large part by assuming that the islands are loads on an unbroken Earth’s crust. . . . The trough [on the northeast] might then be explained as the down-warping of the crust under this load, although it must be recognized that in this case another trough ought to be expected on the south-west side of the island-ridge and nothing is found there. In any case, we may state that gravity does not point towards great disrupture of the crust or to strong disturbances of the normal distribution of the crustal material. This agrees with the absence of earthquake-centres in this area. Our conclusions are based, however, on a few stations only and further evidence will certainly be needed before a final opinion is possible. [Under the Hawaiian island] there seems to be no root at the lower boundary of the crust or, if there is one, it cannot have great dimensions, for else the regional anomalies ought to show stronger deviations than they actually do. So we may conclude that the present material points to a crust which has undergone no shortening at all. This would determine the islands as huge volcanoes piled on the ocean-floor and pressing down this floor by their weight. Their isostatic compensation, therefore, must be of the re gional type. During the later, 1932, cruise Vening Meinesz obtained
F igure 69. Gravity anomalies in a profile across S. Miguel Island. Free-air, long dashes; Hayford, dotted line; Airy, short dashes; Regional, continuous line. T esting Isostasy at Sea 301 anomalies at several points along a north-south line crossing the volcanic island S. Miguel of the Azores. These, with one more anomaly obtained in a former year, appear in the pro file of Figure 69, a section about 600 kilometers long, and the various anomalies are stated in Table 45.
T able 45 GRAVITY ANOMALIES ACROSS S. MIGUEL ISLAND (milligals; International formula)
Distance Number apart Depth Free-air Modified Hayford Airy Regional of station (km) (meters) Bouguer 435 3,900 + 3 6 + 2 5 8 + 5 3 + 5 0 + 4 7 125 436 3,480 - 6 + 185 + 13 + 15 + 18 150 437 0 (P.Delgada) + 152 + 118 + 2 6 + 3 8 + 14 70 438 2,440 + 11 + 132 + 10 + 2 3 + 2 1 125 48 3,610 + 2 6 + 2 3 5 + 5 1 + 4 5 + 5 9
[The profile] shows a decrease of the positive anomalies over a broader zone than the island, which seems to indicate that the decrease is not directly connected with the island itself. In the regional anomalies, the island does not show up; the regional anomaly in Punta Dclgada is + 14 milligals and it is + 18 and + 21 milligals for the neighbouring stations over deep water. So the fundamental assumptions of the regional reduction method seem to be nearer to the actual situation here than those of the other methods, and so we may conclude that gravity appears to indicate the islands as a volcanic load on an unbroken crust. The gravity results for this island are contradictory to the cur rent opinion that volcanic islands in the oceans show a great gravity excess because of the heavy volcanic material of which they are built. (1934 report, p. 102.) A profile, similar in principle, was established across vol canic Madeira, the anomalies being given in Table 46. 302 Testing Isostasy at Sea
T able 46 GRAVITY ANOMALIES IN WEST-EAST SECTION ACROSS MADEIRA (milligals; International formula)
Distance Number apart Depth Free-air Modified Hayford Airy Regional of station (km) (meters) Bouguer 466 5,040 - 6 + 2 8 3 + 18 + 8 - 2 130 467 4,000 + 4 7 + 2 7 6 + 4 7 + 4 3 +29 110 468 3,250 + 8 0 + 2 5 5 + 6 4 + 7 1 +51 100 469 0 (Funchal) + 2 3 0 + 2 0 6 + 6 9 + 7 9 + 26 110 470 4,070 - 2 + 2 1 4 + 2 4 + 2 7 +19 100 471 4,220 + 2 + 2 4 6 + 3 2 + 2 3 +19
Here again the strong positive anomalies “are not confined to the immediate neighbourhood of the island but they ex tend over some distance over the adjoining deep sea. So the excess is probably not related to the direct effect of heavy volcanic material.” The anomalies discovered around the volcanic islands gain in meaning when compared with the anomalies at stations
T able 47 GRAVITY ANOMALIES ON DEEP-SEA VOLCANIC ISLANDS (milligals; International formula)
Locality Elevation Free-air Hayford (meters) Honolulu 6 + 2 1 9 +57 M auna Kea 3,981 + 647 + 188 Maui Island, Hawaii 117 + 2 3 6 — Maui Island, Hawaii 3,001 + 5 0 6 — M auritius 16 + 242 — Jamestown, St. Helena 10 + 2 7 9 +102 Longwood, St. Helena 533 + 2 9 6 ------Ascension Island 5 + 183 — Ascension Island, Green Mountain 686 + 199 — Fernando de Noronha, off Brazil 10 + 2 4 9 — St. Georges, Bermuda 2 + 2 8 3 + 6 4 Testing Isostasy at Sea 303 on these volcanic lands. For this purpose the anomalies at Honolulu and on Mauna Kea, Hawaii (based on the Inter national formula) are listed in Table 47.18 To facilitate further comparison, the table gives free-air and Hayford anomalies (International formula) for some is lands which are remote from lines of measurement of gravity at sea. Commenting on the available data, Heiskanen argues that the wide departures from equilibrium indicated by the mag nitudes of these anomalies means that the islands must grad ually sink until equilibrium is finally reached, the adjust ment being as inevitable as that now approaching perfection in Fennoscandia, which has lost its heavy icecap.19 How ever, field geology gives no evidence of continuing subsi dence. Localized subsidence and localized uplift during earlier geological periods have been proved for many of these enormous piles of lava, but the idea of their systematic sinking at the present time is not supported by geological observations. In fact, many of the older volcanic piles show little or no subsidence for a period of more than a million years. Vening Meinesz has made it more than ever clear that under the loads the lithosphere has bent down, and that there is no evidence of the fracturing and faulting de manded if equilibrium is being established. GRAVITY ANOMALIES AT STATIONS NEAR GREAT DELTAS If thick and extensive delta deposits were accumulated on a perfectly rigid lithosphere which was originally in isostasy, positive anomalies should be found at stations located over the outer slopes of such embankments. Vening Meinesz has supplied valuable first data bearing on this subject of the relation of great deltas to the field of gravity. Table 48 gives the relevant figures for three stations on or close to the visible delta of the Nile. 304 Testing Isostasy at Sea
T able 48 GRAVITY ANOMALIES AT POINTS CLOSE TO THE NILE DELTA (milligals; International formula)
Distance Number of apart Depth Free-air Modified Hayford Airy Regional station (km) (meters) Bouguer 8 (northwest of the delta) 2,020 - 6 4 + 7 0 - 2 3 - 3 4 -2 7 90 10 (northwest of the delta) 620 - 1 8 + 15 - 2 0 - 2 1 -2 7 60 9 0 + 6 + 1 - 1 3 - 1 3 -1 9 (Alexandria)
In comment on the results, Vening Meinesz writes: “These values of the anomalies certainly give no indication of an ap preciable lag in the readjustment of isostatic equilibrium during the deposition of the Nile sediments.” (1934 report, p. 109.) T able 49 GRAVITY ANOMALIES NEAR AND ON THE EMERGED PART OF THE MISSISSIPPI DELTA (milligals; International formula)
Number of station Depth (meters) Free-air Hayford At sea: 16 2.260 -5 6 -2 2 13 1,890 + 19 +21 14 990 + 13 + 6 15 980 + 4 + 7 12 135 + 38 + 13 means, 12-16 + 4 + 5 On land: Elevation (meters) 279 2 + 12 -2 2 280 2 + 4 6 + 15 281 2 +32 + 10 282 2 +25 + 8 283 2 - 9 -2 9 284 2 + 10 - 2 5 26 +21 + 13 means, 5 and 279-284 + 15 - 1 Testing Isostasy at Sea 305 Opposite the Mississippi delta five stations were occupied during the Vening Meinesz-Wright cruise of 1928. The anomalies are stated in Table 49, where also appear the free- air and Hayford anomalies for seven stations located on the emerged part of the delta, these values being taken from the Coast and Geodetic Survey table of 1934. The authors of the report on the 1928 cruise make the fol lowing statement (p. 77 of the Publications of the U. S. Naval Observatory, vol. 13, Appendix 1, 1930): The general conclusion that can be drawn from the few measure ments available is that the Mississippi Delta does not show evi dence of the excess positive anomalies that might be expected if the earth’s crust were of great strength and capable of supporting the extra load. The evidence, so far as it goes, is that the Missis sippi Delta is a compensated load and that compensation is pro ceeding concomitantly with the deposition of the load. This conclusion recalls that of Bowie after his study of the anomalies at the land stations only: The block of the isostatic shell directly under the Delta of the Mississippi is very nearly in isostatic equilibrium. . . . The delta material has been compensated for by a movement of ma terial from the base of the block.20 CONCLUSIONS The development of a good method for measuring gravity at sea was epoch-making in earth science. We have noted some of the discoveries made by this method during fifteen years. One result of the pioneering is proof that the intensi ties of gravity over the ocean—nearly three fourths of the surface of the globe—can be determined with accuracy com parable with that possible on land. Although the study of the marine areas has only begun, it is already clear that no great change in the International formula for the geoidal figure, regarded as a rotation-spheroid, will ever be required. 306 T esting Isostasy at Sea On the other hand, the anomaly fields, as reported by Vening Meinesz, strongly support the idea of approximate triaxiality for the real figure. His table of Bouguer anomalies makes it more than ever certain that there is isostatic balance between continent and ocean. His mean Airy anomalies in the Pa cific and Atlantic regions are smaller than the corresponding Hayford anomalies, indicating that, throughout the world, compensation according to the suggestions of Airy or Heis- kanen dominates over the Pratt-Hayford type of compensa tion. Those more general results of study in submarines mean fundamentally important data for translating anom aly fields into uncompensated loads on earth-sectors, both continental and marine. But other discoveries by Vening Meinesz are no less signifi cant in the study of terrestrial strength. They include: the surprisingly large positive anomalies in the mediterranean sea-basins; the huge negative anomalies over the deeps of the open ocean and over the “strips” of East Indies and West Indies; the algebraic increase of isostatic anomalies in passing from continental shores toward the deep water; and the large, positive anomalies at stations near volcanic islands. The bearing of these various facts on the theory of ideal isos tasy will be considered in chapter 12. Finally, a word may be added about the relation of some of the observations of Vening Meinesz to one of Barrell’s criteria for the strength of the lithosphere.21 So far as they go, the measured values of gravity at stations close to the voluminous Nile and Mississippi deltas show that such great masses of sediment are not likely to provide a test of litho spheric strength. Why the deltas are apparently in nearly perfect isostasy, in spite of their recent origin and compara tively small areas, is an unsolved mystery. If a solution is ever found, we shall doubtless know better how to account for the depressions occupied by the waters of the Gulf of Mexico and the Mediterranean Sea of the Old World. Testing Isostasy at Sea 307
R efer en ces 1. 0. E. Schiotz, “The Norwegian North Polar Expedition, 1893-1896,” vol. 8, 1900, p. 60. 2. O. Hecker, Verdjjent. Geodat. Inst. Potsdam, N. F., No. 11, 1903; No. 16, 1908; No. 20, 1910; also E. Guillaume, La Nature, vol. 22, 1894, pp. 275 and 309. 3. F. R. Helmert, Encyc. math. Wissen., vol. 6, 1910, p. ,125. 4. In chronological order, the writings of Vening Meinesz to the year 1934 are: (a) Determination de la pesanteur en mer, Pub. of the Netherlands Geodet. Comm., 1928; (b) Gravity survey by submarine via Panama to Java, Geog. Jour., London, vol. 71, 1928, p. 144; (c) A gravity expedition of the U. S. Navy, Proc. kon. Akad. Weten., vol. 32, No. 2, 1929; (d) Maritime gravity survey in the Netherlands East Indies, ibid., vol. 33, No. 6, 1930; (e) Releve gravimetrique maritime de VArchipel Indien, Pub. Comm. Geodes. Neer- landaise, 1931; (f) Gravity anomalies in the East Indian Archipelago, Geog. Jour., London, vol. 77, 1931, p. 323; (g) Une nouvelle methode pour la reduction isostatique regionale, Bull. Geodes., Union Geodes, et Geophysique Internationale, No. 29, 1931, p. 33; (h) “Gravity Expeditions at Sea,” vol. 1, Delft, 1932; (i) “Gravity Expeditions at Sea,” vol. 2, Delft, 1934. The results of the work in the West Indies are given in: (a) Pub. United States Naval Observa tory, second series, vol. 13, App. 1, Washington, 1930; and (b) The Navy-Prince ton gravity expedition to the West Indies in 1932, U. S. Hydrographic Office, 1933. 5. See B. C. Browne, Mon. Not. Roy. Astr. Soc. London, Geophys. Supp. vol. 4, 1937, p. 279; F. A. Vening Meinesz, Proc. kon. Akad. Weten., Sept. 25, 1937, and May 28, 1938. 6. G. Cassinis, Rendiconti seminario mat. e fisico di Milano, vol. 8, No. 12, 1934; La crociera gravimetrica del reg. sommergible “Vittor Pisani,” Inst. Idrogr. Reg. Marina, Genova, vol. 13, sep., 1935; L. W. Sorokin, 7me seance, Comm. Geodet. Balti- que, Helsinki, 1935, p. 240. 7. S. W. Visser, Verhand. kon. Magnet, en Meteorol. Observa- toriums te Batavia, Geol. ser., vol. 10, 1934, p. 183; compare discussion of the deep-focus earthquakes in the region, by S. Sibinga (Gerlands Beitraege zur Geophysik, vol. 51, 1937, p. 402). 308 Testing Isostasy at Sea 8. M. Smoluchowski, Anzeiger Akad. Wissen., Cracow, tnalh.- naturw. Kl., vol. 2, 1909, p. 3. 9. E. Horn, Geologische Rundschau, vol. 5, 1914, p. 442. 10. W. Heiskanen, Rapport sur VIsostasie, 6me assemblee generate, Union Geodes, el Geophys. Inlernat., Edinburgh, 1938, p. 14. 11. See M. Ewing, Trans. Amer. Geophys. Union, 18th Ann. Meeting, part 1, 1937, p. 66. 12. H. H. Hess, Proc. Amer. Phil. Soc., vol. 79, 1938, p. 71. 13. H. H. Hess, Trans. Amer. Geophys. Union, 18th Ann. Meet ing, part 1, 1937, p. 75. 14. W. Heiskanen, Rapport sur VIsostasie, 6me assemblee generate, Union Geodes, et Geophys. Internal., Edinburgh, 1938, p. 9. 15. M. Matuyama, Proc. Imper. Acad. Tokyo, vol. 10, 1934, p. 626; ibid., vol. 12, 1936, p. 93; “International Aspects of Oceanography” (ed. by T. W. Vaughan, Nat. Research Council, Washington, 1937), p. 69. 16. See F. A. Vening Meinesz, paper in the “Advanced Report of the Commission on Continental and Oceanic Structure,” presented at the Assembly of the Internat. Union of Geod esy and Geophysics, Washington, September, 1939; also “Gravity Expeditions at Sea,” vol. 2, 1934, pp. 99 and 206. 17. See R. A. Daly, Bull. Geol. Soc. America, vol. 50, 1939, p. 414. 18. See W. Bowie, U. S. Coast and Geodetic Survey, Prof. Paper No. 40, 1917, p. 57. 19. W. Heiskanen, in “Ilandbuch der Geophysik,” ed. by B. Gutenberg, Berlin, 1936, vol. 1, p. 943. 20. W. Bowie, U. S. Coast and Geodetic Survey, Prof. Paper. No. 99, 1924, p. 50. 21. See J. Barrell, Jour. Geology, 1914, vol. 22, p. 36. 10 NATURE’S EXPERIMENTS WITH ICECAPS
INTRODUCTION Many pages have been required merely to outline the argu ments of the geodesists for and against the principle of isos- tasy. This friendly controversy has boiled down to a ques tion of definition of terms. In view of the results of special studies by the geodesists, few investigators now doubt the existence of strong lithosphere and underlying astheno- sphere, or the nearly perfect balancing of lithospheric col umns on the weak supporting layer. The remaining uncer tainties relate to the vertical and horizontal dimensions of the balanced columns, and to the question whether the asthenosphere can permanently support shearing stress. Apparently neither uncertainty can be resolved by the most intense research on deflections of the vertical or on gravity anomalies, although in the final chapter we shall try to fix practical limits for size of balanced columns and maximum limit for the strength of the asthenosphere. In fact, geode sists are now of opinion that they need outside help in secur ing a solution for the double problem. Accordingly, they have begun to apply the results of seismological study of the outer earth-shells, and are seeking information from the geologists about the underground. Long ago geologists suggested an extraordinarily promis ing test of the isostatic hypothesis, but foresaw that they 309 310 N ature’s Experiments with Icecaps could not make the test quantitative without, in their turn, securing co-operation from other specialists in earth science. The addition to needed data is now being made by the geode sists themselves, who in their investigation of the figure of the earth continue systematic exploration with gravimeters. This mode of testing, which illustrates so admirably the value of correlation among specialties, is the subject of the present chapter. The title “Nature’s experiments with ice caps” briefly describes the test. JAMIESON HYPOTHESIS Jamieson’s field evidence for thinness of the lithosphere and great weakness for the asthenosphere was noted in the third chapter. He explained the late-Glacial and post- Glacial upwarpings of Fennoscandia, like those of northern Britain, as cases of isostatic recoil of the lithosphere where it had been temporarily depressed by the weights of the Pleistocene icecaps that covered the respective regions. See Figure 70, which shows the approximate limits of the last N ature’s Experiments with Icecaps 311 Pleistocene icecaps over Fennoscandia, Great Britain, and Iceland. In lively fashion, Jamieson pictured isostatic ad justment, plastic flow of the asthenospheric material, as the weight of each icecap forced this material to move horizon-
F igu rf 71. Isobases for the Rhabdomena Sea stage (about 7000 B.C.). Con tour-interval. 50 meters. At the date given, the salt Baltic Sea extended beyond its present limits and covered the area shown in black. Two remnants of the icecap are indicated with shaded borders. (After Sauramo.) tally away from the glaciated tract. He assumed: (1) concentration of such flow just below the lithosphere; (2) viscosity of the asthenosphere great enough to cause super elevation of the rocky surface in a belt peripheral to the icecap; and (3) reversal of the described topographic changes after the ice melted, with removal of weight.* * T. F. Jamieson, Proc. (Quart. Jour.) Geol. Soc. London, vol. 21, 1865—-brief preliminary statement; more detailed account in Geol. Mag., vol. 9, 1882, pp. 400 and 457. Essentially the same hypothesis was independently developed by N. S. Shaler, who seems to have anticipated Jamieson in fathering the idea of the peripheral bulge (see Proc. Boston Soc. Nat. Hist., vol. 17, 1874, p. 291). 312 N ature’s Experiments with Icecaps
WARPING OF FENNOSCANDIA, PAST AND PRESENT The essential facts concerning the uplift of Fennoscandia are well known, but it is instructive to glance at illustrations of the warping as given in Sauramo’s recent, highly signifi cant paper on the mode of upheaval.1 Three of his maps are here reproduced by kind permission. They show the shorelines and isobases for the early, post-Glacial, Rhab- domena stage (Figure 71), the later Ancylus Lake stage (Figure 72), and the still later Initial-Littorina Sea or LI
F igu re 72. Isobases for the Ancylus Lake stage (about 6500 B.C.). Contour- interval, 25 meters. Area covered by the temporary (fresh-water) lake is indi cated by shading. (After Sauramo.) stage (Figure 73). In general the isobases, if continued be yond the vicinity of the Baltic Sea, where they have been actually located, would doubtless have elliptical ground- N ature’s Experiments with Icecaps 313 plans, roughly concentric with the generalized boundary (terminal moraine) of the Fennoscandian icecap itself.
F igu re 73. Isobases lor the LI stage (about 5000 B.C.). Contour-interval, 10 meters. The Baltic Sea of this date was less extensive than at the stage of Figure 71, as a result of continued upwarping. (After Sauramo.) The respective points of maximum uplift, at 250+, 150+. and 120 meters, are all close to the belt where the burdening ice had been thickest. At the same locus an uplift of at least 200 meters had taken place before the oldest of these three beaches was formed, and the total of the “central” up lift since the last icecap began to diminish is probably close to 700 meters. That the upwarping still continues has been known since the seventeenth century, but it was not until Witting pub lished his masterly study of the records of tide-gages that a 314 N ature’s Experiments with Icecaps close parallelism of the current uplift with the isobases for the late-Glacial and post-Glacial beaches became clear. Figure 74 is a reproduction of his map of 1918. Four years
F igu re 74. Witting’s map showing in millimeters the annual rates of contempo rary uplift in Fennoscandia. later he published another map showing that the rise of old bench-marks since the year 1800 proves nearly the same type and rate of differential movement.2 In 1930 Bergsten reported on data from 25 Swedish tide-gages; in principle his map of the isobases for current warping agrees with those of Witting.3 N ature’s Experiments with Icecaps 315 Further striking evidence is of geodetic character and is contained in Kukkamaki’s summary of the changes of level along the lines of a network of precise leveling in southern Finland.4 Figure 75 is a copy of his map, where isobases
F igu re 75. Map showing in millimeters per century the differential, contempo rary uplift in southern Finland (data from precise levelings). indicate the disleveling of the long belt during the forty years preceding 1938. He made an instructive comparison of the rates of uplift, so determined at five points, with the rates given by tide-gage measurements at the same five points; and both sets of figures were compared with Sauramo’s aver age rates of uplift of the Littorina beach at the five points since about the year 5000 B.C. All the values are entered in Table 50, the unitary rate being 1 centimeter per century.6
T able 50 RATES OF CURRENT UPLIFT AT SHORE-POINTS OF SOUTHERN FINLAND
Locality: Turku Ilango Helsingfors Hamia Viborg Method of measurement: Geodetic 5.4 4.3 3.6 3.8 2.8 Mareographic 5.2 4.0 3.6 4.0 4.0 Geological (Littorina beach) 7.4 5.6 4.7 3.1 1.9 316 N ature’s Experiments with Icecaps Moreover, Sauramo points out that, in the same belt of southern Finland, there is general parallelism of the isobases derived by the geodetic method with the isobases for the water-plane at the end of the first Yoldia Sea stage (a late- Glacial stage), about 9,500 years ago. Figure 76 gives the
F igure 76. Isobases for the Initial-Littorina Sea in southern Finland. (After Sauramo.) run of these lines, and, by comparison with Figure 75, it is seen how closely their plot resembles that of the isobases for the current uplift, in spite of the many complicating factors involved.6 These various studies combine to enforce belief in the highly systematic and long-continued nature of the recoil in Fennoscandia. We now return to the problem of explaining the movement. Jamieson did not generalize his idea to the extent reached by many of his successors, who have regarded, and continue to regard, the disleveling connected with glaciation and de glaciation as strongly confirming the principle of isostasy. A number of geologists do not agree. However, a discussion of their objections will show how vital facts, discovered dur ing the last few years, tend to justify Jamieson’s conclusion.
OBJECTIONS TO JAMIESON’S ISOSTATIC HYPOTHESIS (1) The downwarping of Fennoscandia has been specu latively referred to the purely elastic deforma.tion and QQH- N ature’s Experiments with Icecaps 317 densation of the underlying sector of the earth, as the weight of the burdening ice grew to maximum. The upwarping has been referred to elastic deformation and expansion in the same sector. However, it is supposed, according to this idea, that the elastic effects were enormously delayed, com pleted only after the lapse of many thousands of years. Thus it would be a case of elastic after-working, unaccom panied by plastic flow. An analogy would be found in the behavior of unbaked dough after release of localized deform ing pressure in the mass of dough, a hollow formed by the pressure being shallowed at a slow rate after the pressure is removed. (2) A second suggestion is that the basining under load was accomplished by the recrystallization of the rocks under the icecap, a change giving minerals of increased density and therefore a net vertical shrinkage of the loaded sector. It is further assumed that the consequent basining of the rocky surface was slowly annulled after the ice melted, because a new recrystallization, in the reverse sense, gave net expan sion of the sector and so upwarping of the rocky surface. Neither of these two suggestions, offered as substitute for the isostatic explanation, is adequately supported by known facts, experimental or other, and neither seems to deserve serious consideration. (3) A third objection is more emphasized in geological literature: the warping of the glaciated tract is simply a subordinate phase of the more widely spread, epeirogenic movements, which are quite independent of the positive and negative weights associated with glaciation and deglacia tion.7 Those displacements of the lithosphere, over areas in which localized glaciation is a purely adventitious, unes sential phenomenon, is assumed without any sufficient rea son. It is, of course, manifest that epeirogenic warping has affected the continents since the close of the Paleozoic Era, but one can not safely postulate the continuance of that kind 318 N ature’s Experiments with Icecaps of displacement in the glaciated regions during the last 40.000 years.* This hypothesis, that there is no connection between the upwarping and the deglaciation, shows its full weakness when confronted with field statistics. We might conceive that the observed systematic warping in one or two tracts might be explained by independent epeirogenic movements, but it seems incredible that in a dozen regions the same type of warping should appear as mere accidental products of a stress system that has no vital connection with ice-loads. Yet basining and recoil have been demonstrated in as many widely separated tracts, each having been covered with heavy masses of ice, recently melted away. In some, if not all, of the cases the meltings and warpings began less than 50.000 years ago. With few exceptions there are no signs that the lithosphere outside these tracts was simultaneously disturbed by anything like the same amount. Table 51 gives the uplift of the marine limit in each region; the list was compiled from an earlier publication by the. writer.8
T able 51 UPWARPING IN REGIONS OF COMPLETE OR PARTIAL DEGLACIATION Maximum observed Tract uplift (meters) Scotland...... 30 Iceland...... 120 Greenland...... 146 or more Spitsbergen...... 45 Novaya Zemlya...... 100 Franz Joseph Land...... 30 or more Taimyr region, Siberia...... 15 New Zealand, South Island. .. . 100 + Patagonia...... 40 Antarctica...... 100 Fennoscandia...... 2754- Eastern Canada-Labrador...... 2704- Newfoundland...... 137 * Field studies seem to show that Greenland has been warped by an epeirogenic movement, one unrelated to the partial deglaciation of the great island. See R. A. Daly, “The Changing World of the Ice Age,” New Haven, Conn., 1934, p. 142. N ature’s Experiments with Icecaps 319 In each case the amount of uplift stated is equal to the maximum observed height of the marine limit, and is con siderably smaller than the total non-elastic uplift since the volume of ice began to diminish. One reason for the last statement is the obvious fact that the ocean could not leave any beach-line record of its own level in the area still mantled with ice, while this same area, around the center of former accumulation of ice, was slowly rising with the relief of load. In Fennoscandia and eastern Canada the total non-elastic uplift has been somewhat more than double that respectively indicated in the table. Greenland and Antarctica have lost much ice during the last few tens of thousands of years, and both regions logi cally appear in the table. It is also worth recalling that the seismologists of the Wegener expedition are inclined to be lieve that the rocky surface of Greenland is actually basined, as if by the weight of the existing icecap.9 In spite of complications due to the play of independent forces, the lithosphere has recoiled non-elastically in every region where thick icecaps of wide span have lost much vol ume. Where, on the other hand, the span was small, so that the weight of an icecap could not overcome the bending strength of the lithosphere, warped beaches and other famil iar signs of post-Glacial upwarping should not be found. This is apparently the case with Kerguelen Island and the Faroe Islands. Thus, statistical inquiry seems to confirm the isostatic hypothesis and corroborates the idea that the compensation for topography should be regional. (4) Again, it has been argued that, if the adjusting, iso static flow did occur under Fennoscandia, the outward flow should have taken place near the surface, with consequent erection of a high peripheral bulge not far from the terminal moraine. This theoretical deduction appeared in Jamieson’s original description of his views, and was later accepted as 320 N ature’s Experiments with Icecaps logical by Barrell, the present writer, and many other geolo gists.10 If the deduction were sound, it would be possible to apply another test to the Jamieson hypothesis. For the bulge around the great Fennoscandian tract should have been so high and of such long life that the belt could not fail to show physiographic signs of the former existence of the pronounced bulge. Because the expected effects of the imagined strong bulging are not represented in the existing and post-Glacial patterns of drainage-lines along the edge of the Fennoscandian tract, Schwinner has recently empha sized new doubt about the isostatic explanation of the post- Glacial recoil. However, it now seems that Jamieson was wrong in assuming the adjusting flow to have been so con centrated near the earth’s surface. In 1933 the present writer examined the question as to how the shearing stresses were distributed under any of the major icecaps.11 It was found that the stresses tending to cause outward, horizontal flow had to be concentrated at great depth in the planet. On the assumption that the plasticity of the terrestrial mat ter did not decrease with depth, it was argued that the flow under each icecap was concentrated at great depth. Hence it was concluded that the peripheral bulge must have been both much wider and much lower than it was pictured by Jamieson and nearly all later investigators. Now, however, it seems impossible to ignore the physical implications of the earth’s triaxiality, recently re-emphasized by Heiskanen (see p. 32). The triaxiality can not be a recently developed, short-lived condition. If the geoid is “permanently” triaxial, the greater, deeper part of the earth —a thick sub-asthenospheric shell—is able to bear stresses far greater than the asthenosphere can support. It thus now appears probable, in the writer’s opinion, that the iso static adjustment for the addition of mass and weight by glaciation, or removal of mass and weight by deglaciation, has been accomplished by flow in a relatively thin astheno- N ature’s Experiments with Icecaps 321 sphere, immediately below the lithosphere. If this be true, the viscosity of this weak layer must be small, compared with the mean viscosity of the earth as a whole. The viscos ity of the asthenosphere is now thought to be so low that the super-elevation of the peripheral belt should be small, as field observations show to be the case. Hence the revision of the problem seems to indicate a reasonable way of meet ing this fourth objection to the isostatic hypothesis. (5) Schwinner finds difficulty in accepting Jamieson’s idea because, according to Schwinner, the hypothesis implies a non-elastic basining of the lithosphere all the way to the terminal moraine, the fact being, however, that the basining did not extend so far outward. But when we allow for the comparative thinness of the ice covering the outer 100 or 200 kilometers of the glacial lobes, and also remember the strength of the lithosphere in flexure and shear, the inade quacy of this criterion for the worth of the isostatic doctrine is clear. (6) A more commonly expressed reason why the defor mation of Fennoscandia can not be referred to isostatic ad justment is the supposed late-Glacial interruption of the uplift with periods of subsidence of the rocky surface. How ever, the expert students of this tract now clearly recognize that, during the melting of the last set of Pleistocene icecaps, there was a eustatic, world-wide rise of sea level to the extent of about 100 meters. Much of this flooding of the Baltic region occurred long before the uplift of the lithosphere was completed. Hence it is not surprising that rather wide transgression of the sea took place even while slow uplift of the rocky surface was under way. Without proper guarding on this side, the argument against an isostatic character for the recoil is manifestly inconclusive. Moreover, Sauramo, with first-hand grasp of the relevant facts, has recently summed his own conclusion on the sub ject, in the following words: “The old and well-known idea 322 N ature’s Experiments with Icecaps of land sinkings and transgressions during the late-glacial epoch has not been supported by investigations in the Baltic basin, at least not in the Finnish part of it. On the contrary the land near the ice-sheet has always had a tendency to rise.” 12 Even if general uplift in Fennoscandia were affected by temporary, local subsidence, the isostatic hypothesis would not therefore lose its sanction. The lithosphere is a hetero geneous assemblage of rocks, charged with a complicated system of stresses. Under the conditions one readily im agines that, while the region was being relieved of load by the melting of a highly irregular, lobed icecap, some small part of that region may have been forced up temporarily, too high for equilibrium, and later sunk, to approach equilib rium more nearly. In the meantime, the region as a whole may have been rising without interruption. The local shears observed, so-called “quasi-orogenic” displacements, seem to find herein a fairly general explanation. Sauramo now agrees that Fennoscandia has its “hinge-lines” (better, hinge-zones), analogous to those in North America, where distributive faulting has probably dominated.13 On several grounds, then, this recurring argument against the isostatic nature of the recoil in Fennoscandia should be discounted. (7) Finally, we shall consider an important criterion for the isostatic hypothesis and the statement that the Fen- noscandian case does not meet the criterion. Because the upwarping still continues, there should be defect of mass in the Fennoscandian sector of the globe; consequently the gravity anomalies should there be dominantly negative. It has been thought that this deduction is opposed by actual fact. Such scepticism was possible, though without war rant, when observations on the intensity of gravity were few and far between, but a recent flood of new data seems to show clear satisfaction of the criterion. The only part of the upwarped region already covered N ature’s Experiments with Icecaps 323 with a satisfactory network of gravity stations is Finland. However, the geodetic service of that country has been so active that almost one fourth of the whole area inside the outer limit of the upwarped region can now be discussed quantitatively. Up to the year 1930, the Finnish data were meagre, but in that year Pesonen published the free-air and Bouguer anomalies at 111 stations, distributed through four degrees of latitude and twelve degrees of longitude. Like all his predecessors reporting on Finnish stations, he referred the anomalies to the Helmert 1901 spheroid of reference. In 1937, Hirvonen gave the free-air anomalies at 202 Finnish stations and at about 60 Russian stations, all within the area of upwarping; this time the 1930 International formula was the basis of reference.14 The change from the Helmert formula to the International reduced each anomaly algebraically by about 9 milligals. The free-air anomalies shown on Hirvonen’s map are grouped in a somewhat irregular way, but a glance at the map shows eastern Finland to have mildly positive values, while a broad belt to the west, along the shore of the Gulf of Bothnia, shows decidedly negative values. The relation between absolute value for an anomaly and distance from the center of maximum accumulation of the Pleistocene ice becomes clearer when the average anomalies in three successive zones are compared. The effectively burdening part of the icecap was broadly elliptical, the ground-plan having an approximately north- east-southwest axis. This axis lay about 75 kilometers west of the western shore of the Gulf of Bothnia, and the lines in dicating uniform rates of current uplift are also ellipses with major axes running in the same direction. Hirvonen’s grav ity field was divided into three zones by arbitrarily drafting on his map two elliptical lines, respectively 300 kilometers and 600 kilometers from the central locus of thickest ice, and roughly parallel to the isobases. The average anomaly 324 N ature’s Experiments with Icecaps within each of the three zones was computed and found to have the value given in the fourth column of Table 52.
T able 52 MEAN ANOMALIES IN THREE FINNISH ZONES (milligals)
Width limits, Mean free-air measured in Number of Mean free-air anomaly Zone kilometers stations in anomaly (Heiskanen from the zone (International 1938 triaxial Glacial axis formula) formula) i 0-300 50 -1 4 -24 2 300-600 128 - 4 -14 3 600-800 77 +2 - 6 But we have seen that Heiskanen, using an unrivaled mass of data, has shown how the International spheroid of refer ence can be improved. In 1938 he proposed his latest tri- axial formula, and also gave a biaxial formula which would nearly as well satisfy the gravity observations. (See Table 2.) The triaxial formula differs from the International in the first and second terms, and the longitude term also has to be considered.* Allowing for the ranges of latitude and longi tude in the Finnish region, it appears that the free-air anom alies based on the new triaxial formula are in average 9 milli gals smaller algebraically than those based on the Interna tional. Column 5 of Table 52 gives such corrected free-air anomalies, in average, for the three zones. The corresponding averages for Hayford or other isostatic anomalies would each be about 1 milligal smaller than the values given in columns 4 and 5.| * W. Heiskanen (Vcrojjcnt. Finnischen Geodiit. Inst., No. 26, 1939, p. 104) finds that the curvature of the geoid in central Europe agrees with what should be expected if his triaxial formula is in principle correct. See also his discussion in Publication No. 6 of the Institute, 1926, p. 17. t The relief of Finland is low. Its gravity stations have an average height of only 73 meters; only nine exceed 200 meters in elevation, and the highest is at 261 meters. Manifestly there can be little difference between free-air and isostatic anomaly in this wide area. In a paper published by the writer in the Bulletin of the Geological Society of America (vol. 50, 1939, p. 392), the mean difference for Fennoscandia was estimated at 2.5 milligals, an estimate probably twice too high. N ature’s Experiments with Icecaps 325 Figure 77 gives the free-air anomalies with Heiskanen’s triaxial formula. The stations are represented by dots.
F igu re 77. Free-air anomalies in Finland, based on Heiskanen’s 1938 triaxial formula for the earth’s figure (milligals). The numbers without sign are all negative. The areas with positive anomaly are stippled. Assuming Heiskanen’s bi axial formula of 1938 as basis of reduction, each value would come out at about one milligal algebraically greater. The Hayford means would be similarly affected by the change of formula. Thus, by use of the latest and presumably begt spheroid of reference, the Finnish tract becomes almost entirely negative 326 N ature’s Experiments with Icecaps in anomaly, and Table 52 shows how in general the new means for the three zones decrease algebraically with de crease in distance of station from the locus of thickest ice. It has long been known that large areas underlain by the Rapakivi granite, as well as that including the Aland Islands, are characterized by exceptionally large negative anomalies which as yet lack final explanation. Nevertheless, these and the less significant complications caused by local varia tions of density or of sialic thickness do not change the conclusion that the gravity-gradient in Fennoscandia agrees well with the isostatic hypothesis. Can one really doubt that Nature’s experiment should now be taken more seri ously than ever before?*
RECOIL OF THE GLACIATED TRACT OF NORTHEASTERN NORTH AMERICA If the current deformation of the Baltic region is a case of isostatic adjustment, it is natural to look for relevant data and conclusions within the limits of the Labrador icecap. Since Gilbert described the tilting of the area occupied by the Great Lakes, most geologists have regarded the change as truly homologous with that reflected in the records of the Fennoscandian tide-gages. Later studies by Moore, Free man, and Gutenberg have in principle confirmed Gilbert’s explanation in terms of isostatic adjustment, and have shown that systematic warping is now affecting the lithosphere all the way from Minnesota to New York State.16 Gutenberg found the rate of tilting per hundred kilometers per century to be nearly the same as the corresponding rate in Fennoscandia. He located the hinge-line for the contem porary warping near South Chicago (Calumet lake-gage) * Relatively small areas of positive anomaly may represent local excesses of mass, but these areas would rise because the underlying rock persists in elastic continuity with the lithospheric rock underlying the much larger area character ized by negative anomaly and defect of mass. N ature’s Experiments with Icecaps 327 and about 100 kilometers south of Cleveland, Ohio.* Throughout the length of the hinge-line, as drafted on Gu tenberg’s map (here Figure 78), this line is about 300 kilo-
F igu re 78. Contemporary warping of the Great Lakes region (after Gutenberg). See the text concerning the position of the zero isobase. meters south of the Algonquin hinge-line, north of which plastic deformation of the earth’s crust is known to be under way. Between the old hinge-line and the hinge-line for con temporary warping is the broad belt where the late-Glacial Whittlesey and Algonquin beaches are essentially horizontal. * Mr. Sherman Moore of the United States Lake Survey Office believes that there is no evidence of relative disleveling between Calumet and Milwaukee dur ing the last half-century (personal communication). In any case it is necessary to separate the purely elastic and temporary part of the differential movements in the Lakes region from the permanent part due to plastic yielding of the earth-shells involved. When the proper allowance is made, it appears that the hinge-line for the plastic deformation crosses Lake Michigan no farther south than Milwaukee. Nor does the study of the contemporary warping seem to prove any serious dis placement of this hinge-line from the position favored by Taylor and Goldthwait. For further remarks on the question see following paragraphs in the text. 328 N ature’s Experiments with Icecaps This horizontality would be truly hard to understand if the present tilting of the 300-kilometer belt were due to a plastic reaction of the earth’s crust to relief of ice-load.16 However, there is no problem here if the observed tilting, south of the Algonquin hinge-line, is a purely elastic and temporary effect, to be exactly reversed after another cen tury or so. Such a temporary, elastic tilting is to be expected for two reasons. First, the United States Lake Survey has shown that the Great Lakes lost one to three feet of water during the intervals of time for which the disleveling was measured. This relief of load on the 100,000 square miles (250,000 square kilometers) of lake-covered crust north of the most southerly stations, Calumet and Cleveland, could not fail to produce a purely elastic tilting of the crust all across the belt where the beaches are otherwise essentially horizontal. If, in the future, a slight change of climate should return the missing water to the lakes, there would be an elastic effect exactly annulling the one described, and the beaches would not show even a slight tilting due to the observed motion through the last half-century. A more important reason for the temporary, purely elastic tilting of the belt is to be found in the flexural strength of the earth’s crust. Because of this strength the plastic, non elastic, warping north of the Algonquin hinge-line is accom panied by an upward drag of the crust out to a distance of several hundreds of kilometers, to southward of that hinge line and even far beyond the hinge-line of the contemporary tilting. This purely elastic displacement of the “belt of horizontality” will go on until the stress surpasses the flex ural strength, and then the slightly super-elevated belt will rapidly snap down so as to restore horizontality for the old beaches. Such an adjustment may be expected after some decades of additional tilting, in the future. Repeated ver tical oscillations of the 300-kilometer belt would at no time N ature’s Experiments with Icecaps 329 tilt the old beaches more than a few decimeters per hundred kilometers. There would be no permanent tilting of the beaches. This second, quite temporary, elastic effect is probably the chief reason why the rocky surface under Lake Erie and the rocky surface under the middle third of Lake Michigan have been slightly tilted southward during the last 50 or 80 years. Although there are uncertainties regarding rates and azi muths of movement, the contemporary disleveling of the American tract is seen to be remarkably like that in Fen- noscandia. Again we find close agreement with the older warping, proved by beaches, and here too the rate of uplift increases toward the locus of maximum thickness and weight of the icecap. Such repeated correlations can hardly be accidental, and we may reasonably assume that the upwarp- ing is now going on all around the Labrador-Hudson Bay center of ice a,ccumulation. The question whether this broad area exhibits the theo retically expected defect of gravity and mass can not now be fully answered. Yet even the few measurements of gravity already made suggest an affirmative solution to the problem. All the gravitational data in hand have been compiled by Miller and Hughson in Canada and by the United States Coast and Geodetic Survey.* The Hayford anomalies are given for 170 stations, distributed between the 70th and 80th meridians and between the 45 th parallel of latitude and the terminal moraine to the south. The mean anomalies for the United States territory and for the Canadian territory (In ternational formula, 113.7 km) have been computed and en tered in Table 53, which also records the Hayford anomalies when referred to the 1938 triaxial formula of Heiskanen. * A. H. Miller and W. G. Hughson, Pub. Dominion Observatory, Ottawa, vol. 11, No. 3, 1936; A. H. Miller, ibid.., No. 4, 1936. Relevant tables and maps, not regularly published, have been supplied to individuals by the U. S. Coast and Geodetic Survey, the more complete records bearing the dates 1934 and 1938. 330 N ature’s Experiments with Icecaps
T able 53 MEAN HAYFORD ANOMALIES IN BELT WITHIN THE GLACIATED TRACT OF NORTH AMERICA (milligals)
Number of Mean anomaly referred to formula named: Region stations in average International Heiskanen-triaxial In United States 130 -5 - i i In Ontario and Quebec 40 -8 -15 In Ontario alone 26 -11.5 -17
The anomalies are all negative, and they show some alge braic decrease in passing from south to north, that is, toward the center where the pressure of the heavy icecap was great est. These calculated results are crude, but they serve to emphasize the worth of Jamieson’s essential idea.
NANSEN’S EVIDENCE FROM THE STRANDFLAT Belief in the rule of isostasy was unreservedly expressed by Nansen in two remarkable memoirs dealing with the late- Glacial and post-Glacial warping of Fennoscandia. The first, published in 1922, is entitled “The Strandflat and Isos tasy”; the second, “The Earth’s Crust, its Surface-forms, and Isostatic Adjustment,” appeared six years later.17 Nansen there attributed to isostasy so startling a degree of perfection that even strong advocates of the principle have difficulty in reconciling his argument with the relevant facts of observation outside Scandinavia. However, extreme as may be his statement of the case, his study of the strandflat contains valuable evidence as to the isostatic adjustment of Fennoscandia for the positive and negative loads, respec tively, due to glaciation and deglaciation. The reasoning has weight and represents a test even more purely geological than that furnished by inspection of the gravity anomalies. The low platform along the western and northwestern shores of Norway was given the name “strandflat” by Hans N ature’s Experiments with Icecaps 331 Reusch. It is a belt including thousands of low islands, skerries, and capes, immediately in front of the dissected, old-mountain highland of Norway; this highland rises abruptly from the inner margin of the strandflat, which here and there bears more or less isolated “stacks” or “monad- nocks,” commonly with steep slopes. The width of the belt varies from a few kilometers to 60 kilometers. At its inner limit it has maximum elevation of about 40 meters above sea level, but Nansen distinguished three “levels.” All three are topographic facets cut across the disordered, het erogeneous rocks of Norway. In the southern part of the belt the uppermost “level” is in general 30 to 40 meters above sea level; farther north this facet is somewhat lower and less conspicuous. In the south the lower “level” is about 15 to 18 meters high and along Helgeland of the north is 8 to 10 meters high. The third facet is submerged to a depth of a few meters. A typical cross-profile of the strandflat is given in Figure 79, taken from a large number of sections illustrating Nan-
F igu re 79. One section of the Norwegian strandflat. (After Nansen.) sen’s memoir. This particular profile extends across Smolen Island at about 63° 30' north latitude. Nansen wrote (1922 paper, p. 220): These different levels of the strandflat obviously indicate that the shore-line has stood at different levels during the long periods when the strandflat was developed. We must assume either that the land has risen or that the sea-level has been lowered. 332 N ature’s Experiments with Icecaps In fact, he believed that both causes have operated: It is, in my opinion, probable that the different levels of the strandflat in Norway indicate different interglacial periods of its formation, and mark the levels of equilibrium of the land crust during each of these periods. Owing to the great quantities of rock and debris of the interglacial erosion carried away from the land-surface into the sea by the big glaciers, the land has been somewhat raised by isostatic movement to the new level of equi librium after the disappearance of the ice cap of each glacial period. It is not known how many Pleistocene glacial periods there may have been in Norway. But considering that at least four different glacial periods are now established for Central Europe, it seems hardly probable that there should have been less in Scandinavia. If the strandflat has two distinct levels it seems to indicate that there have been at least three glacial periods in Norway as was already assumed by Oxaal. If there are actually three dif ferent levels, it may indicate four glacial periods. The successive truncations of the rocky formations to form the facets or “levels” are attributed by Nansen largely to the relatively rapid disintegration of the rocks by frost- action during the long, cold intervals respectively introduc ing the glacial stages, the shattered fragments of rock being quickly removed by waves and currents. As noted in the quotation, the isostatic rise of the belt was facilitated by such removal of load, but was chiefly the result of erosive removal of load by glaciers (and streams) over the adjacent Scandinavian highland. Nansen seems not to have noticed that this main cause of upwarping would involve a departure from isostasy in the strandflat itself, but the departure would be slight. The other condition for height of the two upper “levels” is found in the world-wide drop of ocean level when much or all of the Antarctic and Greenland ice was piled on the lands. Nansen thought it probable that each interglacial stage in cluded a prolonged interval of time during which the sea N ature’s Experiments with Icecaps 333 level stood a few meters to perhaps 25 meters higher over the belt of the strandflat than it stands now; it was then that the assumed intensive frost-action hastened the lowering of the rocky surface. In an analogous way Nansen explained the third, sub merged “level” as having been planed during some long period when the ice-caps of the earth were a good deal greater than now. . . . Although there has been an isostatic upheaval of the land since that time, the level of the lowest part of the strandflat has not been raised above the present level of the sea surface. (1922 paper, p. 224.) Nansen’s explanation of the strandflat is thus in contrast with that of Reusch, Vogt, Davis, and others who have thought it to be essentially a plain of marine denudation, made ragged by strong, differential Glacial erosion. Wave cutting of so wide a bench in the hard rocks would require many millions of years, a period of practically perfect stabil ity of the region in its relation to sea level. The genetic process preferred by Nansen could have operated within a total period comprising less than a half million years. It seems doubtful that an initial highland could have been so faceted within such a short period. Nevertheless, while the theory of marine denudation appears reasonable, some part of the faceting may well be understood as due to the special rapidity of frost attack on the rocks along the shore of the ocean. But whatever the origin of the strandflat, its development must have taken many hundreds of thousands of years, Nor way then remaining steadily at or close to a constant level. Moreover, the period of stillstand must have antedated the growth of the last Fennoscandian icecap and also may be reasonably considered to have been a time of nearly perfect isostasy for the region. Nansen assumed the establishment of a similar isostatic condition by the time the weight of the last icecap had pressed down the strandflat along with the 334 N ature’s Experiments with Icecaps rest of the Scandinavian peninsula. Over the strandflat the late-Glacial marine limit is now a few tens of meters to more than 100 meters above sea level. This maximum applies to Helgeland, just south of the 66th parallel of latitude, where the total non-elastic recoil must have been still greater, prob ably 150 meters or more. There as elsewhere the highest late-Glacial beach-line necessarily registers smaller elevation than the whole uplift due to deglaciation.18 Nansen rightly stresses the fact that, after such relatively strong depression of the strandflat, it has risen so much as to restore the iso static balance to essential perfection.* It appears hard, therefore, to resist Nansen’s conclusion that the double displacement of the strandflat has been the result of isostatic adjustment. In any case his purely geo logical criterion needs more attention than it has hitherto re ceived from either geologists or geophysicists, and tends to confirm the testimony of the gravity anomalies in the Fen- noscandian tract.
SUMMARY Two ways of deducing the strength of the asthenosphere have been described. Previous chapters give the details about a static method, the earth’s topography being assumed stable. The present chapter has outlined facts on which may be founded an alternative, dynamic method, involving present instability of the topographic relief. The one method assumes no isostatic adjustment in progress; the other method is based on the discovery of regions where iso static adjustment for loads, negative and recently developed, is actually under way. After noting Jamieson’s explanation of the post-Glacial uplift of Fennoscandia, we have seen that the upwarping * According to W. Heiskancn (VerdJJent. Finnischen Geoddt. Inst., No. 5, 1926 map), the Hayford gravity anomalies along the strandflat, from the 61st to the 66th parallel of latitude, are actually positive. N ature’s Experiments with Icecaps 335 continues today, at a measurable rate. And we have used the Hayford anomalies of gravity in the region to express approximately the span and maximum intensity of the (negative) load causing the uplift. The relations of load and deformation to the stress in, and strength of, the asthen- osphere will be discussed in chapter 12. There the corre sponding evidence for great weakness of the asthenospheric shell will be stated. The apparently inevitable conclusion, thus postponed, is essentially like that of the extreme isos- tasist, Nansen, whose argument from the history of the strandflat in the glaciated tract closes the present chapter.
R efer en ces 1. See M. Sauramo, Comples Rendus Soc. Geol. Finlande, No. 13 (Bull. comm. geol. Finlande, No. 125, 1939); also maps and sections in R. A. Daly’s “The Changing World of the Ice Age,” 1934, chapters 2 and 4. The dates of the stages named in Figures 71-3 of this book are given in round numbers. 2. R. Witting, Fennia, vol. 39, No. 5, 1918; Geografiska An- naler, vol. 4, 1922, p. 458. 3. F. Bergsten, Geografiska Annaler, vol. 12, 1930, p. 21. 4. T. J. Kukkamaki, Verojfent. Finnischen Geodat. Inst., No. 26, 1939, p. 125. 5. The mareographic records are discussed by H. Renquist in a paper entitled “Endogeenisel ilmiot, Suomen maantieteen kasikirja,” Helsinki, 1937, p. 99. 6. See M. Sauramo, Comfles Rendus Soc. Geol. Finlande, No. 13, 1939, p. 8. 7. For a recent statement of the argument, see R. Schwinner, Geol. Rundschau, vol. 29, 1938, p. 12. 8. R. A. Daly, “The Changing World of the Ice Age,” New Haven, Conn., 1934, pp. 141-6. 9. R. A. Daly, ibid., p. 11. 10. J. Barrell, Amer. Jour. Science, vol. 40, 1915, p. 13; R. A. Daly, Bull. Geol. Soc. America, vol. 31, 1920, p. 303. 11. Compare R. A. Daly, “The Changing World of the Ice Age,” New Haven, Conn., 1934, p. 121. 336 N ature’s Experiments with Icecaps 12. M. Sauramo, Comptes Rendus Soc. Geol. Finlande, No. 13, 1939, p. 21. 13. See R. A. Daly, “The Changing World of the Ice Age,” New Haven, Conn., 1934, pp. 124 ff. 14. U. Pesonen, Verojjent. Finnischen Geodat. Inst., No. 13, 1930; R. A. Hirvonen, ibid., No. 24, 1937; see also B. L. Oczapowski’s table of anomalies in Carelia (Gerlands Beitraege zur angewandten Geophysik, vol. 5, 1936, p. 467). 15. G. K. Gilbert, 18th Ann. Report, U. S. Geol. Survey, Part 2, 1897, p. 595; S. Moore, Military Engineer, vol. 14, 1922, p. 151; J. R. Freeman, “Regulation of the Great Lakes (Chicago Sanitary District),” 1926, p. 149; “Earthquake Damage and Earthquake Insurance,” New York, 1932, p. 139; B. Gutenberg, Jour. Geology, vol. 41, 1933, p. 449. 16. See also F. B. Taylor’s statement of the difficulty, in Papers of the Michigan Academy of Science, Art, and Letters, vol. 7, 1926, p. 150. 17. F. Nansen, Videnskapsselskabets Skrifter, mat.-naturv. Kl., No. 11, 1921 (1922); Avhand. Norske Videnskaps. Akad. Oslo, mat.-naturv. Kl., No. 12, 1927 (1928). 18. See R. A. Daly, “The Changing World of the Ice Age,” New Haven, Conn., 1934, p. 138. 11 RETROSPECT
INTRODUCTION Six of the preceding chapters have been concerned with a fundamental question: How great are the departures of the earth from isostatic equilibrium? We desire the answer be cause, from the spans and amplitudes of the uncompensated loads, geophysicists are attempting to find the distribution of terrestrial strength. Only one chapter, the last, has been devoted to another method of discovering that distribution— namely, by study of the earth’s reaction to partial and com plete deglaciation on the large scale. The ratio, six chapters to one, reflects the relative emphasis so far put by geophysi cists on the two methods, and yet the second method may ultimately prove the more efficient, so far as the astheno- sphere is concerned. Both methods should give results in close agreement, if the quantities needed in their application are ascertained. It is not easy to fix those quantities, and a principal reason is that we do not know exactly how to make proper allowance for isostasy. However, a review of con clusions recorded in chapters 5-10 may have value as it em phasizes the fact that useful estimates of the major uncom pensated loads on earth sectors are possible. First, we shall refer once more to the idea for which the best available symbol is the word “isostasy.” The argu ments for a close approach of the earth to ideal isostasy and for comparative thinness of the lithosphere will be sum marized. 337 338 Retrospect A third subject for review will be the difficulty of fixing the areal limits of, and intensities of load corresponding to, actual departures from isostatic equilibrium. Here deci sions are still troubled by uncertainties about: (1) the true figure of the earth; (2) the sparseness of observations on gravity and the deflection of the plumb line, per unit area of the earth’s surface; (3) errors of mensuration and computa tion; (4) the actual modes of compensation; (5) the depth of compensation; (6) the effect of local abnormalities of rock density; and (7) the possibility that individual departures of the lithosphere from equilibrium are temporary and now be ing slowly diminished. These various troubles will be re considered. In spite of them, relatively large areas of one- sign anomaly and one-sign deflections of the vertical seem to have been demonstrated. The testimony of the irreduc ible deviations from isostatic balance as to the distribution of terrestrial strength will be the main theme of chapter 12.
MEANING OF THE WORD “ISOSTASY” It may not be amiss to observe once again what the name “isostasy” does not signify, and what it should signify as a practically useful, if not indispensable, description of a truth of Nature. That there is danger of obscuration for geologist or geophysicist who first approaches the subject of terrestrial strength becomes apparent when quotations from some lead ing authorities are brought face to face. In his last report on isostasy, to the Geodetic Association of the International Geodetic and Geophysical Union (1938), Heiskanen wrote: The isostatic investigations both old and new have proved that in the earth’s crust isostatic compensation prevails, but in such a way that there are both small and also great regions which have not yet reached the isostatic equilibrium. I said in my Lisbon report: “Several parts of the earth’s crust are either already in or tending towards the isostatic equilibrium”, and I am also of the Retrospect 339 same opinion now. It is nearly as useless to study whether the visible mass-anomalies in the earth’s crust are compensated or not as to ask whether twice two are four or not. Much more important is it to study the regions with strong isostatic anom alies because such studies will most further the science. He was no less emphatic seven years before, when he stated his belief in the following words: We can say that for all regions that have been investigated— omitting volcanic regions and the ocean depths—the invisible mass-anomalies thoroughly compensate the visible ones, so that isostatic compensation is no longer an hypothesis but an estab lished principle, which must be taken into consideration in ex plaining geodetic, geophysical and geological problems. Jung and many others agree with the last statement.1 On the other hand, Hinks has said that “the whole trend of modern opinion is towards Airy’s root-compensation and against Pratt’s columnar. This being so, I would urge that the word ‘isostasy’ be dropped.” Hunter is equally drastic: “In view of the implications which have latterly become at tached to the word ‘isostasy’ by unjustified reiterations of its ‘proof,’ I agree that it would be best to drop the word alto gether.” Again he writes: “There is no ‘principle of isos tasy’ in the sense that has often been implied, that is, of Hayford compensation; and it is misleading to use the term.”2 Glennie, who, like Hunter, has furnished much of the proof that large parts of India are out of balance, has reached a similar conclusion. In an abstract of his crust-warping hypothesis, he wrote: “I have endeavoured to prove that the gravity results [in India] are opposed to the Principle of Isostasy.” And elsewhere: Although isostasy as a fact is denied, as an illusion it persists; hence the presentation of gravity results in the form of Hayford anomalies still remains the best method for universal application as a first step towards the investigation of the structure of the Earth’s crust.3 340 Retrospect Is such divergence of opinion necessary? From the be ginning of his investigations Hayford clearly distinguished the ideas bearing the respective names “isostasy” and “com pensation.” For him isostasy meant an approximate condi tion of balance among the parts of the lithosphere, and his type of compensation was a frankly artificial conception, adapted for convenience while attempting to improve the formula for the earth’s figure. His colleague, Bowie, made the same distinction, and showed that in the United States departures from perfect isostasy were even greater than Hayford had found. That most geodesists have not confused the two concep tions is illustrated in the publications of Heiskanen and Vening Meinesz, who accept the principle of isostasy, not withstanding cumulative evidence that Hayford compensa tion is actually less probable than Airy, Heiskanen, or re gional-isostatic compensation or some combination of these competing types. Hunter is prepared to accept Dutton’s hypothesis, and the references to “crust” and “hydrodynamical equilibrium” in Hunter’s paper indicate his belief in the individuality of lithosphere and asthenosphere—the essential items in a use ful, objective definition of “isostasy.” In any case, the suggestion of removing “isostasy” from the vocabulary of science is not justified by any of the pub lished arguments. Geodesists as well as geologists and geophysicists must either retain the word or invent another one in its place. There can be little doubt as to the decision; unless all signs fail, Dutton’s term is here to stay. However, its acceptability and its real value demand a certain vague ness in its definition. Although phrased in terms of litho sphere and asthenosphere, an exact statement of thickness for either earth-shell is now out of the question. To fill present needs the definition should not be founded upon any particular value for the (necessarily small, if not zero) funda Retrospect 341 mental strength of the asthenosphere, or on any fixed opinion about the exact shapes of the equipotential surfaces at great depth in the earth. Clearly those surfaces, like the geoid, have not the simple forms of ellipsoids of revolution, though we have seen that the geoid, even with assumed triaxiality, deviates from the International figure of the earth by no more than about 350 meters. Considerable stress is chronic in the lithosphere, and the asthenosphere can never be quite free from small shearing- stresses, but isostasy implies nothing concerning the amount or distribution of shearing-stress below the asthenosphere. If the smoothed geoid approximates to the triaxial formula suggested by Heiskanen in 1938, there must be notable, “permanent” stress-differences in the earth’s body. How ever, if these are concentrated in the mesospheric shell and are absent in the overlying asthenospheric shell, their exist ence in no wise invalidates the essential conditions for isos tasy, namely, restriction of compensation for irregularities of topographic relief to a strong lithosphere that rests on a layer with vanishingly small strength. Nor should a generally acceptable definition of isostasy be based on any fixed values for the densities of lithosphere and asthenosphere, or on any one theory of compensation for the earth’s topography. After all these exclusions, “isostasy” can nevertheless rep resent a conception of fundamental and practical impor tance. The conception is twofold. “Ideal” isostasy implies that compensation for topography is complete at some mod erately deep level, the completeness being possible because the asthenosphere has no strength whatever, so that, below the depth mentioned and above any assumed, strong meso spheric shell, the material is in hydrostatic equilibrium. “Actual” isostasy is the close approach of lithosphere and asthenosphere to the conditions respectively described. Both ideas, “ideal isostasy” and “actual isostasy,” must be 342 Retrospect coupled with the certainty that in general compensation for topography is regional.
PROOFS OF CLOSE APPROACH OF THE EARTH TO IDEAL ISOSTASY The fact that topography is as a rule nearly compensated becomes more and more certain as the two main criteria for its truth continue to be applied by the geodesists. As we learned in chapter 2, the criterion based on the actual shape of the geoid was the first to be seriously applied. Direct studies of Andes, Himalayas, and Pyrenees in turn yielded affirmative results, later corroborated by the Hayford-Bowie investigations of plumb-line deflections and correlated geoid in the United States. And now even peninsular India, so admirably treated by the Survey of India, has supplied evi dence of the same kind. For though the actual geoid in India is decidedly warped out of any ellipsoidal figure, the humps and hollows are truly small compared with what they should be if there were no isostatic compensation for High Asia, the deep Indian Ocean, and the peninsula itself. The other test devised by the geodesists has been made with still greater thoroughness. For the first time, Hayford and Bowie conducted systematic examination of a widely extended territory with respect to the variation of the in tensity of gravity across-country. They discovered that the intensity did not increase with height of station at any thing like the rate to be expected if there were no isostatic compensation for the United States topography. Later Heiskanen’s work in the Caucasian, Norwegian, and other fields led him to conclude that the parts of the free-air and Bouguer anomalies at mountain stations, depending on height of station, are strongly positive and negative respec tively, as they should be if isostatic equilibrium is closely approached.4 In general, Bouguer anomalies are enor mously reduced by assuming Hayford’s extreme type of Retrospect 343 compensation—compensation that is perfectly local and uniform to a uniform depth below the rocky surface. This reduction is almost as great if the compensation be assumed absent within a circle with radius of 50 to 100 kilometers ffom each station. Another of the mathematical tests used by Hayford and Bowie involves the sums of the squares of the anomalies, and its application confirmed the reality of thin lithosphere and weak asthenosphere. Heiskanen then showed that the anomalies computed ac cording to the Airy and Heiskanen types of compensation, not only in the United States but also in Switzerland, Nor way, and Japan, led to the same conclusion. When, finally, Vening Meinesz proved the prevalence of huge, positive Bouguer anomalies over all the deep oceans, in contrast with the big negative Bouguer anomalies over the continents, the last doubt about the existence of general isostasy, with the meaning here preferred, was removed. For any one mode of isostatic compensation, the most probable thickness of the lithosphere is that which gives the smallest increase of anomaly with increase of station height. When this principle is applied, all types of compensation indi cate thicknesses for the lithosphere not exceeding 100 kilo meters. It is likely, if not indeed inevitable, that the actual compensation is a variable combination among the Pratt, Airy, Heiskanen, Vening Meinesz, and “anti-root” kinds, but there is no apparent reason to suppose that the thickness of the lithosphere would, with any of the combinations, come out at any higher figure. That the lithosphere is relatively thin is further suggested by its flexibility, as noted in the last chapter, where the be havior of the tracts unloaded by the melting of Pleistocene ice was described. Of particular importance in the main problem of this book are two questions: (1) What are the maximum spans and intensities of the uncompensated loads on the earth? 344 Retrospect (2) How much of each load can be borne by the lithosphere alone? These queries will be given detailed attention as we continue the general review.
RELATION OF GRAVITY ANOMALY TO SPHEROID OF REFERENCE Several of the preceding chapters contain quantitative illustrations of the change of anomaly with change of the figure of the earth assumed for the computation. Table 54 shows how the values of mean anomalies for large regions are similarly affected. Here the comparison will be made with respect to Hayford anomalies, but the algebraic differ ence found for any one region would be nearly identical if the anomalies had been calculated on any other hypothesis of compensation, including zero compensation. The stated values of anomaly are only approximate, but accurate enough to show that regional anomalies can not be safely taken to indicate uncompensated loads on the corresponding sectors of the earth, until the correct spheroid of reference has been determined.
T able 54 MEAN HAYFORD (T = 113.7 KM) ANOMALIES WITH THREE DIFFERENT SPHEROIDS OF REFERENCE (milligals)
Inter Heiskanen Number of Approximate Approximate Helmert national triaxial Region stations limits in limits in 1901 formula formula averaged latitude longitude anomaly of 1930 of 1938 U. S. A. 448 25°-49° 65°-125°W. + 8 - 5 - 1 to - 2 Finland 202 65°-69° 20°- 30°E. + 2 - 6 -16 E. Africa 87 5°N.-9°S. 3 0 40°E. - 9 -26 -16 The uncertainty about a choice for the best spheroid has special significance in a dozen or more exceptionally wide regions of one-sign anomaly, the individual anomalies having been computed by the International formula. Most of the cases have already been mentioned, but for convenience re Retrospect 345 spective means for the Hayford and Airy anomalies, in some major instances of apparent departure from isostasy, are en tered in Table 55. The table also lists approximate values for the corresponding mean anomalies found when Heis- kanen’s 1938 triaxial formula is substituted for the Interna tional formula. In all these cases, the substitution reduces the anomalies numerically and diminishes the spans and intensities of the apparently uncompensated loads on the lithosphere. We remember, too, that the triaxial spheroid of reference has been derived from the latest and fullest data available. This important relation between anomaly field and actual load will be further considered in the next chapter. Throughout that study we shall keep steadily in mind that the triaxial formula gives no more than an approximation to the true figure of the earth, and that change of the formula is to be expected with increase of the facts of observation, especially in the world-circling belt between 10° north lati tude and 10° south latitude. Nevertheless, Heiskanen’s triaxial formula of 1938 is not likely to be so far from the truth that it can not be used for roughly estimating the actual departures from isostatic equilibrium. Parenthetically, it may be remarked that any error in the assumed absolute value of gravity at Potsdam, the world base, has no appreciable effect on the relative positions of isanomaly lines. On the other hand, errors in determining gravity at a local base station, by swinging a pendulum at this station and also at Potsdam, would give corresponding errors in fixing the limits of anomalous areas within the coun try concerned and sizes of anomalies in those areas.
NEED OF GREAT EXTENSION OF THE GRAVITATIONAL SURVEY We saw that the oceans, extending over 70 per cent of the earth’s surface, can never be triangulated by the method 346 Retrospect
T able 55 MEAN ANOMALIES IN FOUR MERIDIONAL BELTS (milligals)
Mean anomalies Number International Triaxial formula of formula (rough values) stations Hayford Airy Hayford Airy (T = 113.7 (D = 40 km) km) POSITIVE FIELDS I Adjacent to meridian passing through one end (A) of major axis of Heis- kanen’s equatorial ellipse (locus at 25° west longi tude) 1. At sea only 76 +31 +25 + 6 0 2. Western Scotland 20 + 14 — - 1 — 3. Great Britain 59 + 8 + 11 -7 -4 II Adjacent to meridian passing through point an tipodal to A (locus at 155° east longitude) 1. Western Pacific, at sea 172 + 20 + 15 -5 -1 0 2. East Indies, at sea 281 + 15 + 18 + 6 +9 NEGATIVE FIELDS I Adjacent to meridian passing through one end (B) of minor axis of Heis- kanen’s equatorial ellipse (locus at 115° west longi tude) 1. Pacific coast-belt, U.S.A. 51 -28 -2 2 -16 -1 0 2. Mexico 42 -2 0 — - 4 — II Adjacent to meridian passing through point an tipodal to B (locus at 65° east longitude) 1. Arabian Sea 6 -2 1 -26 0 -5 2. India (south of 28°, north latitude) 306 -2 4 — -7 — used on the lands of the other 30 per cent, while the use of gravimeters have no such restriction. Contour lines for re Retrospect 347 siduals of the deflections of the vertical can be drawn for about one per cent of the earth’s surface. Isanomaly lines can be drawn with anything like accuracy for no more than two or three per cent of that surface. Manifestly, therefore, it is impossible to be sure that geodesists have already found the area that represents the maximum, “permanent” depar ture from isostasy. On the other hand, the sampling of the planet so far accomplished, especially in the northern hemi sphere, has been statistically rather favorable. The diag nosis has been made in regions that are widely separated and of great individual extension in latitude and longitude; and also along one complete line of circumnavigation. Consid ering all the facts in hand, it seems probable that the north ern hemisphere will not be found to have deviations from lithospheric equilibrium greater than those represented by India, Turkestan, and the ocean “Deeps.” Still more impos ing abnormalities of the kind may, of course, be ultimately discovered in the southern hemisphere, where observations of gravity are now so few and sparse. Meantime geophysi cists continue to estimate terrestrial strength from areas of one-sign anomaly in the northern hemisphere, and the geologist can not do better than follow their lead, while sharing doubt as to the exact dimensions of the load implied by any one of those areas. Among the regions where there is immediate need of new determinations of gravity over wide networks of stations are: Central Asia, the Tonga Deep and vicinity, Norway and Sweden, Hudson Bay and adjacent land, Greenland, Ant arctica, and the site of the former Lake Bonneville. The first two deserve attention because they have given some of the largest anomalies yet recorded on continent and ocean; the other six, because of their relations to the dynamic test of isostasy, represented by the geologically recent changes of loads of ice and water on limited sectors of the globe. 348 Retrospect
EFFECT OF ERRORS OF MENSURATION AND COMPUTATION The detailed discussion of Hayford, Bowie, and others indicates that the value given for anomaly or deflection re sidual may contain a small error due to the use of simplified expressions for the attractions of zoned topography and zoned compensation; and other small error due to imperfec tion in the measuring apparatus. Some of the errors in curred by adopting the Hayford-Bowie original systems of zoning have been diminished by increasing the number of zones. Accuracy in pure computation has been enhanced by the recent availability of special tables of reference com piled by Lambert, Cassinis, Heiskanen, Bullard, Vening Meinesz, and others. The calculations on which these tables are based have been governed by notable mathe matical refinements. To some extent the various errors cancel one another, and it is safe to say that most of the anomalies given in Heis- kanen’s world Catalogue are not vitiated by large errors of mensuration and computation. Such as remain will not greatly affect the size of any area of one-sign anomaly or affect the corresponding values for the intensity of gravity in that area.*
EFFECT OF CHANGING THE ASSUMED TYPE OF ISOSTATIC COMPENSATION Let us consider a major area of one-sign anomaly, the anomalies being successively computed according to the Hayford, Airy, Heiskanen, Putnam-regional, Vening Meinesz-regional, and “anti-root” types of compensation. Provided the center of gravity of each compensation remains * This statement applies also when allowance is made for the attraction of the material between geoid and spheroid, that is, for the “indirect reduction.” (See p. 126.) At a station a large vertical distance between geoid and spheroid may mean greater stress in the lithosphere than a smaller distance would mean. This difference is at maximum if the asthenosphere can bear no shearing-stress. Retrospect 349 approximately the same, the mean anomalies do not greatly differ.* (See p. 62.) Heiskanen, Vening Meinesz, Bul lard, and others have illustrated this general fact by actual calculation and report. Tables 56 to 59 give examples. The anomalies are based on the International formula for the earth’s figure. T able 56 MEAN ANOMALIES (milligals) AND MODES OF COMPENSATION
Means for 313 stations, Means for 48 stations, Type of compensation U.S.A. in general Pacific-coast belt of the U.S.A. Hayford (T = 113.7 km) + 6 -2 4 Airy {D = 40 km) +9 - 2 0 Airy (D = 60 km) +5 -23.5 Heiskanen (D = 50 km) +9 -18.5
T able 57 MEAN ANOMALIES FOR 71 STATIONS, CAUCASIAN REGION (milligals) Hayford (T = 113.7 km) +53 Hayford (T = 156.3 km) +49 Hayford (T = 184.6 km) +45 Hayford-regional (no compensa tion to 166.7 km; T = 113.7 km) +55 Airy (D = 77.2 km) +45 Airy (D = 63.8 km) +50
T able 58 MEAN ANOMALIES FOR 11 STATIONS, HARZ MOUNTAINS (milligals) Hayford {T = 80 km) +36 Hayford (T = 113.7 km) +34 Airy (D = 40 km) +36 Airy (D = 63.8 km) +33 * F. A. Vening Meinesz (“Gravity Expeditions at Sea,” vol. 2, Delft, 1934, p. 19) has shown why the isanomaly lines in a very extensive field of one-sign anomaly are little changed in position when any of the standard hypotheses of compensa tion is substituted for any other of those hypotheses. On the other hand, Hay- ford, Airy, or any other type of isostatic anomalies, based on the assumption of perfectly local compensation, can not indicate the distribution of mass underground as accurately as it can be indicated by isostatic anomalies, based on some form of regional compensation. 350 Retrospect
T able 59 MEAN ANOMALIES (milligals)
76 176 26 Station Station Station stations, stations, stations, 324. 179, 435, off Type of Compensation eastern western Banda E. Indian Java S. Miguel Atlantic Pacific Sea strip Deep Island Hayford (T = 113.7 km) +31 + 2 0 +55 -168 -103 +53 Airy (D = 40 km) +25 + 15 +50 -174 -105 +50 Vening Meinesz-regional (sial 25 km thick) + 20 + 19 +65 -164 -127 +47 It seems clear that the center of gravity of compensation is in general no deeper than 40 to 50 kilometers below sea level, and also that the actual compensation for topography is a combination of most, if not all, of the types above named. Thus isostasy, in the sense of approximate balancing of seg ments of a relatively thin lithosphere, may be taken as dem onstrated. But there is no such assurance of ideal isostasy, which has been defined in terms of a thin lithosphere resting on an asthenosphere with zero strength. Figure 10 shows how the assumption of a compensation tailing-out to great depth will give anomalies nearly identical with those com puted on the assumption of a strengthless substratum. Hence the geodetic data alone, while indicating great weak ness for the asthenosphere, can not specify its actual degree of strength. However, we are to see that a synthesis of the gravimetric results and geological observations in the gla ciated tracts does suggest a decidedly low limit for the pos sible strength of the asthenosphere.
EFFECT OF CHANGING THE ASSUMED DEPTH OF COMPENSATION Tables 56-8 also recall the fact that a large regional anom aly of Hayford, Airy, or Heiskanen type is little altered by considerable change in the assumed depth of compensation. Thus, once again, it seems best to believe that broad areas of one-sign anomaly represent cases of regional compensa Retrospect 351 tion, and again the question arises whether any part of the support of these loads is to be credited to strength in the asthenosphere.
EFFECT OF LOCAL ABNORMALITIES OF DENSITY OF ROCK While Bowie, Barrell, White, Chamberlin, Oldham, and others have shown how a local anomaly is diminished or wiped out altogether by allowing for the gravitational influ ence of unusual densities for rock in the immediate vicinity of the station, the same explanation can not account for wide areas of one-sign anomaly.5 Such correction is indeed neces sary at the negative belt of southern California and at the Ganges alluvium, and may have some importance in the case of a few broad, positive belts; but in general the correc tions fall far short of removing these anomalous areas from the world map. The net effect is in some moderate degree to narrow each belt, and correspondingly to decrease some what the maximum anomaly and mean anomaly. The re sidual values are what will interest us when we study their testimony to the distribution of terrestrial strength.
HOW PERMANENT ARE AREAS OF ONE-SIGN ANOMALY? For a given region of anomaly, is the indicated lack of balance stably supported by strength of materials, or is the lithosphere slowly yielding so that both span and intensity of load will ultimately shrink by important fractions? Here generalization is manifestly impossible. The glaciated tracts of northwestern Europe and northeastern North America are rising, as if isostatically, though in each case the intensity of pressure indicated by gravity anomalies is com paratively small. The powerful earthquakes in the ab normal Tongan, Japanese, and Turkestan regions may mean secular approach of each toward equilibrium, but, if so, when 352 R etrospect will the strength of the lithosphere stop the movements, and how great will be the residual anomalies of gravity in each region? These last questions must remain open. On the other hand, it does not seem likely that the regional anom alies characterizing the Hidden Range of India, the southern trough of India, the negative strips of East and West Indies, the Pacific-coast belt from California to Alaska, and many volcanic areas of the Hawaiian and Saint Helena type are being appreciably or essentially diminished by isostatic adjustment.
R efer en c e s 1. W. Heiskanen, Amer. Jour. Science, vol. 21, 1931, p. 29; K. Jung, Zeit.f. Geophysik, vol. 14, 1938, p. 27. When the galley proofs of the present book were being read, J. P. Delaney (Science, vol. 91, 1940, p. 546) an nounced the discovery that four centuries ago Leonardo da Vinci had grasped the essential ideas of isostasy and of isostatic adjustment for the secular erosion of mountain chains. 2. A. R. Hinks, Geog. Journal, vol. 78, 1931, p. 439; J. de G. Hunter, ibid., p. 455; Mon. Not. Roy. Astr. Soc., Geophys. Supp., vol. 3, 1932, p. 50. 3. E. A. Glennie, Mon. Not. Roy. Astr. Soc., Geophys. Supp., vol. 3, 1932, p. 176; Prof. Paper 27, Survey of India, 1932, p. 28. 4. W. Heiskanen, in Handbuch der Geophysik, edited by B. Gutenberg, Berlin, vol. 1, 1936, p. 894. 5. See J. Barrell, Amer. Jour. Science, vol. 48, 1919, p. 286; Jour. Geology, vol. 22, 1914, p. 221; D. White, Bull. Geol. Soc. America, vol. 35, 1924, p. 207; R. T. Chamberlin, ibid., vol. 46, 1935, p. 393; G. P. Woollard, Trans. Amer. Geo phys. Union, 18th Ann. Meeting, 1937, part 1, p. 96; S. Burrard, Survey of India, Prof. Paper No. 17, 1918. 12 STRENGTH OF THE EARTH-SHELLS
INTRODUCTION We have dwelt at length on the complex of facts, working hypotheses, and deductions bearing on the idea of isostasy. The purpose has been double: to furnish an abstract of the widely scattered literature on the subject, and to assemble the geodetic data on which estimates of the actual variation of strength along the earth’s radius and along underground levels have been chiefly founded. In the following discus sion of these estimates and of their implications in geology and geophysics, we give first place to the facts of gravim etry, because the investigators of terrestrial strength have emphasized most the testimony of anomalous fields of gravity. After brief reference to the pioneer researches of G. H. Darwin and Love, the likewise path-making studies of Bar- rell and Jeffreys, which are more directly concerned with the actual anomalous areas, will be considered. Darwin assumed elastic competence for the whole earth and computed approximately the stresses involved if the topographic relief is not at all compensated by appropriate distribution of density. Love made a similar computation after assuming compensation for topography, complete at moderate depth. Barrell, relying on Darwin’s mathematical analysis and assuming elastic competence from surface to center of the globe, sought to reconcile the principle of isos tasy with the continued existence of local loads on the litho- 353 354 Strength of the Earth-Shells sphere. Jeffreys, extending Darwin’s mathematical treat ment, evaluated the stresses corresponding to the uncom pensated loads. He first assumed the earth’s mantle to be elastically competent throughout, and then worked out the values of the stresses expected in the lithosphere if the as- thenosphere has zero strength. He found that in this sec ond case the lithosphere has to be much stronger than in the first case, where the asthenosphere could theoretically carry a large fraction of each load. The results of Jeffreys’ discussion will bring us face to face with a crucial question: can the lithosphere, under a regional load, continue to bear the stresses in the unbalanced sectors of the earth—stresses other than those borne by the sub- asthenospheric material—if the asthenosphere is thoroughly weak? Manifestly no answer is possible until we know the dimensions of the load. Because of the abundance of ob servations in India, and also because the inequalities of mass are there specially imposing, particular reference will be made to the Hidden Range and adjacent gravity troughs. In chapter 8 we learned how different the anomalies be come when the reference figure of the earth is changed from a rotation-spheroid to a triaxial spheroid. It will be noted that other major fields of anomaly are also automatically diminished in span and intensity by the change of reference figure. Nevertheless, even the revised spans and ampli tudes of the Indian fields of one-sign anomaly still imply stress in the lithosphere that approaches the maximum de- ducible from observed gravity on any continental sector. The stresses implied by the greater anomaly fields in oceanic sectors will be similarly discussed. Whether the lithosphere, unaided, can bear such loads permanently depends on the effect of the actual pressures and temperatures on the lithospheric material. Our infor mation is here incomplete, but seems to permit the hypothe sis that the asthenosphere is really devoid of strength. This Strength of the Earth-Shells 355 hypothesis can be neither proved nor disproved by appeal to gravimetry. However, the idea becomes tolerable when we look once more at the gravity anomalies in mobile Fennos- candia and eastern Canada. There we shall find evidence that the asthenosphere is in fact extremely weak, and that the lithosphere under these tested regions has an effective thickness smaller than 100 kilometers. Evidence for horizontal variation of the thickness of the lithosphere and for its variation during past eras will be presented. Such changes mean corresponding variations in lithospheric strength. Extreme weakness for the asthenosphere is further sug gested by the modes of displacement associated with moun tain-building and with igneous action, and appears recon cilable with the reality of deep-focus earthquakes and warped peneplains. Finally, the strength of the sub-asthenospheric shell and an assumed deviation of its surface from the shape of a rota tion-spheroid will be given hypothetical explanation. For this layer we have Washington’s convenient name “meso sphere” or, better, “mesospheric shell”—a coinage more logically conceived than the older synonym “centrospheric shell.” 1
STRESSES CAUSED BY DEPARTURES FROM ISOSTASY The first comprehensive study of the stresses set up in the earth’s body by local, superficial loads was that of G. H. Darwin.2 As just remarked, he assumed fundamental strength throughout the planet and no isostatic adjustment for the loads whatever. To make the mathematics tract able, he assumed uniform elastic constants, uniform density, and loads in the form of zonal harmonics, that is, alternating positive and negative loads with the transverse profiles of regular, symmetrical waves. When treating the harmonics of high degree (small wave-lengths), he was able to simplify 356 Strength of the Earth-Shells the computation by neglecting the curvature of the earth’s surface, his analysis here referring to infinitely long, har monic loads on a semi-infinite, plane solid. Darwin found that, while the stress-difference at the mean surface is zero, the stress-difference at any point under ground depends on the vertical distance of the point below the mean surface and has constant value, whether the point at the given depth is under a crest, under a trough, or under any other part of the wavy surface. The direction of the stress-difference revolves at a uniform rate along a vertical section at right angles to the crest-lines. The maximum
F igure 80. Barren’s diagram of stresses due to harmonic loading. stress-difference is at a depth equal to 1/27r of the wave length, and has the value of 2gDH/e, where g is the force of gravity, D is the density of the rock composing the load, H is half the total height of each wave, and e is the base of the Napierian logarithms. Barrell graphically illustrated Darwin’s results for har monics of high degree.3 Figures 80 and 81 are essentially copies of Barrell’s drawings. Figure 80 shows how the stress-difference changes direction systematically in passing from crest to trough, the wave-length being 200 kilometers and the height of each wave being 5 kilometers. The change of value for the stress-difference as depth increases is indi cated by horizontal shading. Strength of the Earth-Shells 357 Figure 81 shows to scale the curves of the stress-difference for two wave-lengths, one at 200 kilometers and the other twice as great. It is seen that doubling the wave-length, other things being equal, much more than doubles the stress-
Figure 81. Change of field of stress, caused by change of wave-length in harmonic loading. (After Barrell.) difference at any depth below that of 100 kilometers from the surface. Assuming that Bowie’s isanomaly map of 1912 gives the intensities and spans of unbalanced loads on the lithosphere within the limits of the United States, and reasoning also from the likewise meager data regarding the uncompensated ocean Deeps, Barrell made rough estimates of the probable distribution of strength to the depth of 400 kilometers. These estimates were phrased in the form of ratios, as shown in Table 60. The transition from lithosphere to astheno- 358 Strength or the Earth-Shells sphere was thought to be gradual and to be accomplished between the 100-kilometer and 200-kilometer level.4 Jeffreys has discussed Darwin’s problem in a more gener alized form. The result was to show that, if there is no re striction on the vertical distribution of strength, it is possible to support one of the harmonic loads with a stress-difference equal to about 90 per cent of the maximum deduced by Darwin. However, “the stress-differences are distributed through a greater range of depth than on Darwin’s theory,
T able 60 BARRELL’S ESTIMATES OF RATIOS OF STRENGTH AS IT VARIES WITH DEPTH Lithosphere Depth in kilometers Relative strengths 0 100 20 400 25 500 30 400 50 25 100 17 Aslhenosphere 200 8 300 5 400 4 and attain their maximum at three different places, one of which is at the outer surface below the greatest elevations and depressions. This makes it possible to understand how fractures can extend up to the free surface, where, on Dar win’s theory, there is no stress-difference.” 5 Love attacked a quite different problem—the magnitude and distribution of stresses produced by harmonic loads on the lithosphere, the loads being measured by the departures of the topography from the geoid and compensated according to Hayford’s assumptions. The depth of (the purely local) compensation was assumed to be two per cent of the earth’s radius; the material below that depth was assumed to be Strength of the Earth-Shells 359 under hydrostatic pressure. To get quantitative results, Love assumed a special, admittedly artificial law of density in the lithosphere, and then evaluated the stress-differences expected if the relief of the rocky surface be a spherical har monic of the fiftieth degree. In this case the wave-length is 400 kilometers. Taking 2.7 as the mean density of the lithosphere, he found the maximum stress-difference to be about 260 kilograms per square centimeter, if the wave-crests be 4 kilometers higher than the troughs. The maximum stress-difference is thus equal to about half the weight of a column of granite which has half the height of one of the topographic waves; this maximum is located at the mean surface and beneath the crests. Darwin’s solution for a similar harmonic loading gave a maximum stress-difference of about 410 kilograms per square centimeter, with location 80 kilometers below the mean surface. Of special interest is Jeffreys’ analysis in the case where a thin crust is supposed to rest stably on a denser layer of in definite thickness and in the hydrostatic state. When a local load is placed on this crust, the crust bends down until the upward pressure of the substratum, coupled with the elastic reaction of the crust itself, produces a state of equilib rium. With harmonic loading it appears that the corre sponding maximum stress-difference in the crust is approxi mately gDHL/irh, where L is the wave-length and h is the thickness of the crust. From the formula the values of the maximum stress- differences have been computed on the supposition that h is 60 kilometers and 2.7 is the density (D) of the loading rock. The results are shown in Table 61. If h is 75 kilometers, all values of the Table will be 20 per cent smaller. We can not doubt that considerable burdens of small span 360 Strength of the Earth-Shells are stably borne by the lithosphere alone. But if, in accord ance with the conception of ideal isostasy, the asthenosphere be supposed to have no strength, it becomes a serious ques tion whether the lithosphere is able to support the great ver tical pressures represented by any one of a dozen major fields of anomaly. If the span of the load is many times the thickness of the lithosphere, the situation is analogous to that of a loaded, horizontal beam, fixed at one end but free at the other end. Another analogy is that of a thin, hori-
T able 61 MAXIMUM STRESS-DIFFERENCE IN A “THIN, FLOATING CRUST” (kilograms per square centimeter)
II (meters) L = 100 km L — 200 km L = 400 km L = 600 km L = 1,000 km 100 14 28 56 84 140 200 28 56 112 169 281 300 42 84 169 253 421 400 56 112 225 337 562 500 70 140 281 421 702 zontal plate, held firmly along its margin and weighted, with maximum intensity of load not far from the center. Other things being equal, the maximum shearing-stress in the beam increases with the square of the length of the beam; in the thin plate the maximum shearing-stress increases with the square of the radius of the plate. In both cases the maxi mum stress is a direct function of the intensity of the load. These relations, coupled with the older experimental data regarding the strength of rock under pressure, led Barrell and Jeffreys to reject the idea of infinite weakness for the asthenosphere. They thought it necessary to assume some strength in the earth down to the depth of many hundreds of kilometers. Barrell assumed finite strength all the way to the center. (Compare Table 60 and Figure 81.) Jeffreys assumes finite strength throughout the silicate mantle, some 2,900 kilometers thick. Barrell concluded that at the 100- Strength of the Earth-Shells 361 kilometer level the strength is equal to a stress of at least 200 kilograms per square centimeter. Jeffreys, also basing his deduction on fields of gravity anomaly, gets a minimum value of the same order, and, from the study of deep-focus earthquakes, has been led to postulate strength much like that of quarry granite (if not as much as 1,000 kilograms per square centimeter), all the way down to the 600-kilo meter level at least.6 DIMENSIONS OF STABLE AREAS OF ONE-SIGN ANOMALY Except by accident, a Hayford, Airy, Heiskanen, or re gional-isostatic anomaly does not exactly represent a truth of Nature. If, however, such an anomaly differs from zero by more than 10 or IS milligals in either the positive or nega tive direction, that anomaly creates suspicion of a local lack of isostatic balance. The suspicion becomes much strength ened when the anomalies for other, adjacent stations have the same sign as the first and are of comparable size. Hence maps giving isanomaly lines with suitably chosen contour- interval are indispensable, if departures from isostasy are to be estimated from observations of gravity. For any large area of strong anomaly the line of zero anom aly is only moderately shifted by changing the underlying hypothesis of compensation, a given rotation-spheroid of reference being, however, retained throughout. Positive areas remain largely positive; negative areas, largely nega tive ; and the algebraic range between positive and negative maxima of anomaly is not greatly changed. The debate about the strength of the earth-shells has cen tered around the mass of observational data gathered in the United States and in India. Hence the following discussion will refer to certain relations found in these two countries, where alone systematic and comprehensive work, leading to homogeneous results, has been done on a truly grand scale. 362 Strength of the Earth-Shells Anomaly Areas in the United States. From the lim ited United States data supplied by Hayford and Bowie up to the year 1912, Barrell pictured the anomaly fields of the United States in the following words: Upon these broad regions of mean anomaly are superposed smaller and better-defined areas of more than mean anomaly, negative and positive areas occurring in the same broad region. These smallei areas are inclosed by the 0.020 anomaly contour [20-milligal contour]. They commonly range from 300 to 400 kilometers across, 200 to 250 miles, but the maxima which reach above 0.040 are much smaller. The limits of regional isostasy appear then to vary with the amount of the load. Well-defined areas 200 to 250 miles in breadth may stand vertically 800 to 1,600 feet on the average from the level giving isostatic equilib rium, and their central portions reach still higher values. They represent the limits of regional isostasy discussed in an earlier part [of Barrell’s series of papers on terrestrial strength]. But these are superposed on broader areas which may extend for a thousand miles or more and lie as much as 400 to 800 feet either above or below the level for equilibrium. Stresses given by loads of this order are then not restricted in area to the limits set for higher values. (See Figure 33, p. 163.) The size of the areas of intenser stress reveals the capacity to which the earth can carry mountain ranges uncompensated by isostasy. The size of the areas of weaker stress shows the capac ity of a considerable portion of a continent to lie quiescent while the surface agencies carry forward their leveling work. This is the present state of this particular continent after a geologic period of world-wide notable vertical movement and adjustment. It is not likely, therefore, that these loads measure the maximum stress-carrying capacity of the earth. They may be more in the nature of residual stresses which the earth can hold through periods of discharge of stress. East of the Cordillera there has been but little local differential movement and these areas have lain in crustal quiet for long geologic ages, being subject only to broad and uniform crustal warping of moderate amount. It is to be presumed, therefore, that the strains which exist in such regions by virtue of the regional departures from isostasy are of ancient date and well within the limits of crustal strength.7 Strength of the Earth-Shells 363 However, the large increase in the number of gravity sta tions occupied in the United States since 1912 shows the need of revising Barrell’s conclusions, for with the newer observations has come evidence that the spans and ampli tudes of the anomalous areas are smaller than those assumed by Barrell. Elsewhere the present writer has described sev eral examples of the necessary changes in the isanomaly
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' . - 2 I 1 Q 9 8 l'Q»‘ F igu re 82. The change of anomaly belts in Wyoming, caused by increase of number of stations occupied. map.8 Here only one will be presented. Bowie’s 1917 map of Hayford anomalies indicated a rectangular area in Wy oming as positive except for a small fraction in the north west corner. The area measures 550 kilometers by 350 kilo meters. When the Hayford anomalies supplied in 1934 by the United States Coast and Geodetic Survey for the same region were plotted, the positive part of the rectangle was found to be broken up into three positive belts alternating with three negative belts. (See Figure 82.) Moreover, the mean 1917 anomaly for the whole rectangle was + 28 milli- 364 Strength of the Earth-Shells gals, while the mean became only + 14 milligals when based on the fuller information of 1934. This illustration shows how uncertain must be any deduction regarding terrestrial strength from an anomaly map made from observations at widely separated stations. And a second caveat should be filed. By the very nature of the mode of derivation, the Hayford anomalies are not likely to represent the field of gravity or the uncompensated loads with accuracy. Nor can any other hypothesis of com pensation, if made the sole basis for reduction, be relied upon to furnish much closer approx'mation to reality. This statement is seen to be specially justified when we consider the comparative smallness of the mean anomaly (of order of 20 milligals) in any of the broader anomalous areas read out of the 1912 map by Barrell. Further, as already suggested, the facts of dynamical geology appear to compel belief in composite types of compensation, types which have never been used in isostatic reduction. Hence it is still impossible to be sure of the real span and real amplitude of any anom alous belt in the United States; in every case a large percent age of error must be allowed for, if trustworthy geophysical conclusions are to emerge from the anomaly map. On the other hand, some of the United States belts, characterized by smaller span and larger mean anomaly, would doubtless remain anomalous, with sign unchanged, even if the isostatic reduction were founded on perfect knowledge of the distribu tion of rock densities. It is these irreducible areas that are going to engage attention as we proceed with the problem of the earth’s strength. Mechanical Conditions in Peninsular India. A glance at Figures 43 to 51 will recall the vital facts in the case of India. There departures from equilibrium are ex ceptionally clear and are proved by both warped geoid and anomaly map. From the Gangetic trough to the crest marked in Figure 44, the geoid has a total rise of about 60 Strength of the Earth-Shells 365 feet, and it sinks by about the same amount along the trough-line passing near Madras. The “wave-length” is not far from 1,300 kilometers. Figure 49 shows the Hay- ford anomalies, based on the 1930 International formula and recorded along the same cross section of the peninsula, as almost entirely negative. The range of values is a little over 100 milligals. The situation becomes still more thought-provoking when we remember that Vening Meinesz found negative Hayford anomalies all across the Arabian Sea, 2,500 kilometers in width. Apparently, therefore, negative anomalies here dominate over a total area much greater than, for example, the huge glaciated tract of Fennoscandia. And yet there is no evidence that the lithosphere under India and the Arabian Sea is being upwarped. The fact that Fennoscandia, though less (negatively) loaded than the Arabian Sea-India region, is being upwarped, as if by isostatic adjustment, emphasizes the need of examining the Asiatic field with par ticular care. The 1930 International formula is a close representation of the smoothed results of measurement of gravity so far made over the earth as a whole. Hunter, Glennie, Bomford, and other officers of the Survey of India have proved that this formula does not agree with the gravitational data se cured over their peerless network of stations. They have found a better fit when Helmert’s 1901 formula is used for the spheroid of reference, and a still better fit with a formula called “Survey of India II.” Let us compare the Hayford- anomaly fields corresponding to the three formulas. We have already seen that, with each of the two formulas last named, the peninsular region, so dominantly negative with the International formula (Figure 49), becomes broken up into three areas, one positive and the others negative (Figure 50). The three areas are roughly coincident with the Hidden Range arch and flanking troughs, displayed on 366 Strength of the Earth-Shells the map of geoidal contours (Figure 44). In principle a similar tripartite division of the peninsular region appears when Heiskanen’s 1938 triaxial spheroid is made the basis of reduction. For convenience all four formulas are repeated in Table 62.
T able 62 ALTERNATIVE SPHEROIDS OF REFERENCE FOR THE INDIAN FIELD 0 = latitude. A = longitude (positive when east of Greenwich meridian) International: 70 = 978.049 (1 + 0.0052884 sin2 0 — 0.0000059 sin2 20) Helmert, 1901: 70 = 978.030 (1 + 0.005302 sin20 - 0.000007 sin2 20) Survey of India II: 70 = 978.025 (1 + 0.005234 sin2 0 — 0.000006 sin2 20) Heiskanen, 1938: 70 = 978.0524 [1 + 0.005297 sin2 0 - 0.0000059 sin2 20 + 0.0000276 cos2 0 cos 2 (A + 25°)] Special significance attaches to the values of the Hayford anomalies based on the Heiskanen formula. At the equator and 65° east longitude, where the minor axis of the equa torial ellipse emerges, a Hayford anomaly becomes 24 milli- gals larger algebraically than that calculated for the same point from a rotation-spheroid of equal volume. Allowing for the average latitude (about 20°) and average longitude (about + 77°) of peninsular India, the triaxial formula gives + 17 milligals as this necessary change in the mean Hayford anomaly. However, the correction would be some what more south of the Hidden Range and somewhat less over the Gangetic plain. When the new isanomaly-lines are drawn on a map, the plot is much like that made from anomalies calculated by the Helmert 1901 formula (see Figure 50, p. 239). Thus, the difficulty of reconciling the Indian situation with American and other evidence for great weakness of the asthenosphere is much assuaged. Not only is every Hay ford anomaly based on a rotation-spheroid increased alge braically by about 17 milligals, but the total area with nega tive anomaly is nearly halved. Where the International Strength of the Earth-Shells 367 formula demands a dominantly negative field from Ceylon to the Himalayas, the Heiskanen formula gives a broad; positive, Hidden Range belt and the two gravitational troughs. The span of the load represented by one-sign area of anomaly is enormously reduced—in proportion even more than the amplitude of the load-pressure implied by gravita tional inequality is reduced. The stress-differences implied by the sizes and distribution of the Hayford anomalies would be further cut down, if Glennie’s “normal warp-anomalies” represent reality more nearly than the Hayford anomalies represent it. Glennie arrived at the warp-anomalies after allowing for the neces sarily regional nature of isostatic compensation. He as sumed no compensation out to a radial distance of 120,000 feet or 22.5 miles from each station. He adopted the Sphe roid of India II as basis of reduction, a formula which we have seen to give, for India, a geoidal surface almost coincident with that described by Heiskanen’s triaxial figure. The contours for the warp-anomalies are shown in Figure 51, where the belt of the Hidden Range (stippled) is wider than in Figure 50. Each warp-anomaly to the south of the Hid den Range is about 10 milligals less negative than the corre sponding anomaly when computed from the Helmert or Heiskanen formula with local compensation assumed. The range of anomaly from trough to trough is little changed, but the deduced upward pressures tending to warp the litho sphere into a position of equilibrium are smaller than before, and the correlative downward pressure at the Hidden Range is somewhat larger. Final judgment as to the magnitude of the stresses should take account also of the actual irregularities in each field of anomaly. The maps show that the broad positive belt is interrupted by small negative areas and by long, bay-like, negative re-entrants. These negative patches mean local excess of upward pressure by the asthenosphere, excess 368 Strength of the Earth-Shells whereby the tendency of the positive belt as a whole to sink is partly offset. It is as if the positive Hidden Range load has partial support by so many “pillars.” The strong, negative Hayford anomaly of the Indo-Gan- getic belt is in part clearly referable to the low density of the thick alluvium, and to that extent does not represent un compensated load on the sector.* The southern trough is wider, and contains little alluvium of specially low density. However, there are two reasons why the lithospheric stresses may here be no greater than those under the northern trough. First, the maximum and average anomalies are about 20 milligals smaller in the southern area. Secondly, as Figures 50 and 51 show, this belt is interrupted by at least one posi tive area; such an area may mean excess of weight. If it does mean that, it represents a “sinker,” tending to balance some of the upward pressure exerted by the asthenospheric material under the belt. On the assumption that the Indian field is actually tripar tite, we shall later try to estimate the maximum stress-differ ences in the lithosphere, if this earth-shell has to bear all of the stress due to the uncompensated loads. But beforehand it will be well to note outstanding tests for the validity of the triaxial formula, and also to list the greater lithospheric loads on earth-sectors outside of India. If Heiskanen’s triaxial spheroid does closely represent the true figure of the earth, the anomaly fields of the world, found when reductions are based on the International sphe roid, should include a broad, strongly negative, meridional belt following the 115th meridian of west longitude (opposite * According to J. De G. Hunter ar.d G. Bomford (Geodetic Reports, Survey of India, vol. 6, 1931, p. 104), precise leveling shows that parts of the alluvial plain of northern Bengal and Bihar have been rising at the rate of 0.05 foot per year, relatively to a point near Calcutta and thus close to the southern edge of the al luvium. This conclusion, which assumes accuracy of the levelings, 70 years apart, suggests the question whether isostatic adjustment may he in process of easing the stresses in the lithosphere under the Gangetic trough. Or is this movement the result of the horizontal pressure which is responsible for the thrusts along the Himalayan front? Strength of the Earth-Shells 369 the Arabian Sea-India belt following the 65th meridian of east longitude), and two broad, strongly positive, meridional belts centered respectively along the 25th meridian of west longitude and the 155th meridian of east longitude. These deductions are in accord with observed facts, which we shall now proceed to examine. All four belts are among the wid est fields of one-sign anomaly yet found, when the anomalies are derived by the International formula. (See Table 55.) In every case, maximum anomaly and mean anomaly are considerably reduced by the use of the Heiskanen formula, and to that extent it becomes easier to believe that isostatic balance all over the world is nearly as perfect as it is in east ern North America and in Europe. To that extent, the problem of the distribution of strength in the earth’s body is simplified.* A n o m a l y F ie l d a l o n g t h e P a c if ic C o ast o f N o r t h A m e r ic a . Figure 33 represents with fair accuracy the field of negative anomaly paralleling the Pacific shore between the Mexican and Canadian boundaries. The anomaly map of Canada by Miller and Hughson shows that this great negative belt continues to at least the sixty-first parallel of latitude. Its minimum length is therefore 3,500 kilometers, the width being about 1,100 kilometers in maximum and 600 kilometers in average. Throughout the belt as mapped, the * The reader will, of course, understand that the Heiskanen spheroid, like the International spheroid, is a figure obtained by smoothing the humps and hollows of the earth’s actual figure, and can not express the geoid in other than a general ized way. The triaxial formula will need revision, especially after more stations are occupied in the southern hemisphere, and also especially after many more stations close to the equator have been occupied. Nevertheless, it is significant that great additions to the observational data between 1928 and 1938 have occa sioned relatively little change in the co-ordinates of the triaxial figure deduced by Heiskanen (see Table 2). It is at least a question whether drastic change of the formula will ever be required, except in the term giving the longitudes of the points where the axes of the equatorial ellipse emerge at the geoid. Professor Heiskanen (personal communication) suggests that here the uncertainty may be plus or minus 10° or possibly as much as plus or minus 20°. In this book, all reductions based on the 1938 formula may, therefore, be in error, but in general the signs of the corrections would not be changed by using an improved longitude term. 370 Strength of the Earth-Shells anomalies are of the Hayford type, based on the 1930 Inter national formula (T, the depth of compensation, at 113.7 kilometers). They reach their highest value (— 65 milligals) in the United States, where also the belt is widest. Hence attention will be confined to this part. Table 63 gives for all of the 51 United States stations the mean anomalies computed by the International formula and respectively based on the Hayford, Airy, and Heiskanen laws of isostatic compensation.
T able 63 MEAN ANOMALIES, PACIFIC-COAST BELT IN THE UNITED STATES Kind of anomaly Size (milligals) Hayford (depth of compensation 113.7 km)...... —28 Hayford (depth of compensation 96 km)...... —26 Hayford (depth of compensation 56.9 km)...... —17 Airy (sea-level thickness of sial 40 km)...... —22 Heiskanen (sea-level thickness of sial 50 km)...... —21 The indicated defect of mass is hardly to be explained by abnormalities of density of rock near the surface. If, on the other hand, the defect of mass represents a corresponding negative load borne by the lithosphere alone, this earth-shell would be stressed to a degree comparable with that expected in the Indian segment, when the Indian anomalies are com puted and interpreted on the same basis. But the Pacific marginal belt of North America is nowhere far from the meridian where the short axis of the equatorial ellipse of Heiskanen’s triaxial spheroid emerges.* If his formula be made the basis of reduction, the averages of Table 63 would be less negative by 10 to 15 milligals. Moreover, the width of the negative belt would be diminished by at * That meridian is only 5° from the central meridian of California. In this connection it may be noted that, as may be seen at p. 133 of Heiskanen’s world Catalogue, 42 stations in Mexico give a mean Hayford (T = 113.7 kilometers) anomaly of —19.7 milligals. Since the average west longitude is nearly 100° and the average latitude is about 20°, this Mexican region would give a mean anomaly pf only about —4 milligals, if the Heiskanen formula were used. Strength op the Earth-Shells 371 least one half. Such decrease of anomaly and narrowing of the belt would mean a much smaller maximum stress-differ ence in the lithosphere than that deduced from the anomaly field mapped on the basis of the International formula. The residual negative anomaly may be reasonably ex-
F igu re 83. Hayford anomalies in the eastern part of the North Atlantic. plained, at least in part, by the “coast effect” described on p. 297. A n o m a l y F ie l d o f t h e E a s t e r n A t l a n t ic a n d A d ja c e n t L a n d . We now turn attention to the two meridional belts where strong positive anomaly is expected to appear, if the International spheroid is used for reference, while the true figure of the earth is assumed to be really the 1938 tri- axial spheroid of Heiskanen. A large part of the belt traversed by the 25th meridian of west longitude is underlain by the water of the Atlantic, and 372 Strength of the Earth-Shells there the isostatic anomalies, computed by the International formula, have the values shown in Figure 83. Table 35 gives mean anomalies in the eastern Atlantic between 0° and 50° of west longitude. If based on the Heiskanen formula, they would be much smaller. For example, this decrease would be 31 milligals at the equator and at 25° west longi-
T able 64 MEAN ANOMALIES IN LAND AREAS ADJACENT TO THE 25TH MERIDIAN OF WEST LONGITUDE
Approx Number Mean imate Range in Range in Kind of of anom anomaly mean Area latitude longitude anomaly alies av (Interna anomaly eraged tional (triaxial formula) formula) Western Scot land 56° to 60° -5 ° to -8 ° Hayford 20 + 14 - l (T = 113.7 km) Great Britain 50° to 60° 0° to -8 ° Hayford 59 +8 -7 11
(< U u (( > 59 + 11 -4 (D = 40 km) tude, and about 21 milligals on the same meridian and at 45° of north latitude. Table 64 gives for adjacent western Scotland and Great Britain as a whole the respective mean anomalies.* It is seen that the means become closer to zero by the change to the triaxial formula. * The means for Great Britain were computed from the individual anomalies recorded in Heiskanen’s world Catalogue. For western Scotland, the data were found in a paper by E. C. Bullard and H. L. P. Jolly (Mon. Notices, Roy. Astron. Soc., Geophys. Supp., vol. 3, 1936, p. 473). The mean Airy anomaly in France (D — 40 km), as derived from the world Catalogue with the International spheroid as basis for calculation, is +10 milligals. On the same basis, Norgaard’s 400 stations in Denmark and over the Cattegat give the mean Hayford anomaly (H = 113.7 km) at +9 milligals. This mean becomes nearly zero if Heiskanen’s 1938 triaxial spheroid be used. See G. Norgaard, Geodaet. Inst. Copenhagen, Meddelelse No. 12, 1939, for an account of this remark ably dense network of stations. Strength of the Earth-Shells 373
A n o m a l y F ie l d o f t h e W e s t e r n P a c if ic . Because of the complexity of the investigated region of the western Pacific, with respect to intensity of gravity, an average for any type of anomalies can hardly give a satisfactory test of Heiskanen’s triaxial formula. Nevertheless, Table 35 shows that the means of the anomalies at 172 stations are all posi tive and therefore tending to favor the formula for the earth’s figure. For .on this side of the earth the meridian where the long axis of Heiskanen’s equatorial ellipse emerges is at 155° east longitude, while the 172 stations are distributed in a meridional belt bounded by the 120th and 180th meridians of east longitude. Allowing also for the latitudes of the sta tions, we find that the mean Hayford anomaly would be come nearly zero if re-computed by the triaxial formula. S u m m a r y . The statistics of the western Pacific belt are not so compelling as those referring to the belt that includes California, the belt of the eastern Atlantic region, or the belt that includes India, but the signs and magnitudes of the mean isostatic anomalies (International formula) in all four belts are approximately those expected if the Heiskanen triaxial spheroid of 1938 is a good picture of the geoid. De rived by this formula, the mean and maximum anomalies in each of the four belts are significantly smaller than those computed by the rotation-spheroid. With the great diminu tion of the four inequalities of gravity goes implied diminu tion of the intensities of stress within the lithosphere. A n o m a l y F ie l d s o f t h e M editerranean Se a s . The ninth chapter described essential facts regarding still another set of marine areas having prevailingly positive anomalies of gravity. These areas are nearly coincident with as many deep and wide mediterranean basins, typified by the Banda and Celebes basins of the East Indies (Figures 58 and 59), the Gulf of Mexico (Figure 56), the Caribbean Sea (Figure 62), and the Tyrrhenian Sea (Figure 55). Vening Meinesz, who established the fact that this gravi 374 Strength of the Earth-Shells tational condition is common among the deep mediterranean basins the world over, sensed therein another major problem for the isostasist, and suggested a solution. He had found that the anomalies in each basin tend to become more posi tive as the water becomes deeper. He accepts the conclu sion of Umbgrove and Kuenen, that the East Indian basins originated in geologically recent time, and that the respec tive areas originally had continental character. He notes the difficulty of explaining the drastic sinkings by assuming sufficient increase of density for the lithosphere in the same regions, whereby isostatic equilibrium might have been brought about. He writes: “In that case it might be asked why the crust has not subsided enough for quite re-establish ing the equilibrium.” The query indicates that in his opin ion the lithosphere is too weak to bear the positive loads matching these fields of anomaly. By a process of exclusion he was led to explain both the subsidence of the sial and the residual positive anomaly by the presence of appropriate, downward thermal-convection currents. A downward current in the substratum must indeed bring about excesses of mass which give rise to positive anomalies at the earth’s surface. At the same time the surface of the substratum above the sinking current must be lower than that above the ris ing current and so the subsidence of the area agrees likewise to this supposition.9 Manifestly, the convection hypothesis is based on the sup position that the substratum (asthenosphere) has little strength, if any at all. It appears, therefore, that Vening Meinesz is a believer in something like what we have called “ideal isostasy.” Although this is not the place for full discussion of the con vection hypothesis, it is necessary to point again to a diffi culty in the way of its acceptance. The cause of the convec tion is described as thermal, and thus dependent on a density gradient established by cooling from above or heating from Strength of the Earth-Shells 375 below, or by both methods simultaneously. In any of the cases the gradient must be extremely low and the potential correspondingly small. But it seems highly probable that the asthenosphere, like so many of the larger igneous intru sions which can be studied at the earth’s surface, is stratified according to intrinsic, or chemically determined, density. The increase of intrinsic density with depth may be at an exceedingly slow rate and yet sufficient to offset completely the feeble effect of the temperature gradient on density. As already remarked, Vening Meinesz assumes a density of 3.3 for the asthenosphere, a value appropriate for crystal line peridotite, and yet he supposes the down-dragging cur rents to follow the laws of viscous liquids. The manifest difficulty of securing adequate weakness in the astheno sphere disappears if the material is actually vitreous. If we assume that material to be chiefly oceanitic and peridotitic, as suggested in chapter 1, we seem to have within sight an explanation for the mediterranean basins and for their posi tive anomalies—an explanation founded on a static condi tion rather than on a hypothesis of continuing convection. The arrangement of earth-shells now visualized implies potentiality for “major stoping” of the deeper, denser rock of the lithosphere and for the injection of “ultra-basic” magma into this shell. Effects of such instability would be most pronounced in and near zones of mountain-making. During orogenic revolutions the underthrusting and stoping of the lithospheric rock would compel the rise of the astheno- spheric melt, and ultimately far toward the surface. Is it possible that the orogenic disturbance has thus added spe cially dense rock to the lithosphere, in amount sufficient to develop mediterranean basins by isostatic adjustment? Is it also possible that the cooling induced by underthrust and stoping under broad orogenic belts has there so thickened the lithosphere as to cause subsidence and basining of the surface? 376 Strength of the Earth-Shells In principle, Barrell favored an affirmative answer to the first question, though he supposed the heavy magma to have come from chambers isolated deep in the otherwise crystal line asthenosphere, and not from a continuous vitreous sub stratum.10 Any segments of the lithosphere, basined be cause of injection of abnormally dense rock, would, after isostatic adjustment was completed, remain basined indefi nitely. So to produce deep basins in formerly continental areas, like those of the East Indies (per Umbgrove and Kuenen), the Tyrrhenian Sea (per E. Suess), and the Gulf of Mexico (a probable case), would demand enormous intru sions, even if all were peridotitic. The alternative static condition for the basining—namely, that due to thickening of the lithosphere through oro- genic chilling—is not to be ruled out of consideration, but it implies impermanence for each basin developed in this way. For in the course of millions of years the isotherms would be restored nearly to their original positions, and the chilled segments of the lithosphere would expand, with obliteration of the basin form. Finally, it is conceivable that both injection of heavy rock and thickening of the lithosphere may have co-operated to develop the mediterranean basins. Needless to say, these speculations can lead to no definite conclusion, but it does seem that the hypothesis of convec tion should be put into competition with the other two hy potheses just described. It may also be remarked that, if the lithosphere were weighted by enough crystallized, “ultra- basic” rock to produce perfect isostasy, the basins would still show positive anomalies. Anomaly Fields of the Open-ocean “Deeps.” Grav ity anomalies are specially large over, and in many cases near, the ocean “Deeps.” Most of these long, narrow troughs are situated immediately in front of the major moun tain arcs rimming the Pacific basin. Similarly the Brown- Strength of the Earth-Shells 377 son Deep follows the arc bearing the island of Porto Rico. The relation of Deep to mountain chain is systematic and ap parently genetic. In the following brief discussion it will be assumed that the Deeps are downward fracture-warps, caused by the same tangential compression as that responsi ble for the folding and thrusting in the respective chains of mountains; also that, before the deformation, each region was in isostasy, the downwarped lithosphere being simatic and originally covered with four to five kilometers of water. Since the Deeps show depths of six to ten kilometers, this downwarp hypothesis implies the existence of strong nega tive anomalies along the axes of the Deeps, and correlative, positive anomalies along at least one side of each trough. Both deductions agree with the observations of Hecker in the Tonga region and of Matuyama over the Japan (Nippon, Tuscarora) Deep. Other examples are listed in Table 65, which gives data for sections across the Mindanao, Yap, Java, and Brownson Deeps. (See also Figures 63-6.) T able 65 GRAVITY ANOMALIES AT OCEAN DEEPS (milligals; International formula)
Approx Maximum Name of Deep imate depth at width stations Range of values of anomalies (km) (meters) Free-air Hayford Airy Mindanao 200 8,740 -198 to +270 +21 to +134 -58 to +140 Yap 100 7,690 -154 to +288 — 23 to +76 -39 to +63 Java (section 14 of Ven- ing Meinesz) 200 6,690 -148 to +37 -83 to +45 -11 to +35 Brownson 200 8,000 -270 to +36 — 103 to +55 — The values entered for the two kinds of isostatic anomalies are of little significance, because all four troughs are far from being isostatically compensated. This fact is proved by the Bouguer anomalies at the occupied stations with deepest 378 Strength of the Earth-Shells water. Table 34 shows that with isostasy a unit of (modi fied) Bouguer anomaly over the open ocean corresponds to about 17.5 meters of water. Using this figure as a divisor, approximate values for the Bouguer anomalies at the trough stations of deepest water, isostasy assumed, have been com puted. The second column of figures in Table 66 gives the results. The third column gives the Bouguer anomalies actually found by Vening Meinesz; the fourth column, the respective differences. These differences are so great that comparatively little compensation can be assumed to exist directly under the troughed forms. It looks as if the free-air anomalies give a better idea of the defect of mass under each Deep than the isostatic anomalies (with local compensation) give. T able 66 BOUGUER ANOMALIES AT OCEAN DEEPS (milligals; International formula)
Depth of water, Modified Modified Name of deep maximum at Bouguer Bouguer Difference stations occupied (Vening (isostasy (meters) Meinesz) assumed) Mindanao 8,740 +236 +500 264 Yap 7,690 +353 +440 87 Java 6,690 +242 +380 138 Brownson 8,000 +270 +455 185 Moreover, as the gravity profile is followed from the axis of each trough to a comparatively short distance from its margin, the free-air anomaly has rapid algebraic increase, passing through zero and ultimately reaching a high positive value. Hence it is clear that each abnormality of mass is located near the surface, that is, within the lithosphere. The whole departure from isostasy is much greater than that indicated by the negative field alone. If the Deeps are stable elements of the earth’s topography, they furnish minimum values for the strength of the (simatic) lithosphere in the areas of the open, deep ocean. Strength of the Earth-Shells 379 Anomaly Fields Surrounding Volcanic Islands. Similarly the isostatic anomalies at stations on and near the volcanic islands of the deep sea should not be taken, offhand, to represent the real uncompensated loads centered at the islands. It seems likely that these loads are better indicated by the huge free-air anomalies, and that the isostatic com pensation is broadly regional. The most telling observa tions are those made at the Hawaiian stations. The main island of Hawaii itself is the emerged portion of a pile of rock with minimum diameter exceeding 350 kilometers and height of about 10 kilometers. On Mauna Kea, more than 4 kilometers above sea, the gravity anomaly after correction for elevation (International formula)' is + 659 milligals. At the shore the free-air and Bouguer anomalies are doubtless not far from their measured values, + 213 milligals and + 163 milligals, at Honolulu on Oahu Island. It is prob able that only a relatively small part of this gigantic relief is locally compensated. Barrell’s translation of a statement by Helmert may be quoted: For the Hawaiian Islands it must be concluded on the whole that a part of the mass gives rise to positive gravity disturbances and only the remainder is isostatically compensated. If the disturb ances were produced solely by the mass of the islands the values of the [free-air and Bouguer] anomalies would be somewhat greater than they are found.11 The load of Hawaii Island seems to have greater vertical intensity than that of any known load on the continental sectors of the globe. From the Hawaiian case, as well as from that represented at the Tongan flexure, Barr ell arrived at a minimum estimate of the strength of the sub-Pacific “crust” : “The oceanic crust can sustain a harmonic wave-length of 400 kilometers with an uncompensated amplitude measured by 4,000 meters of rock.” But he found the few available data to “suggest 380 Strength of the Earth-Shells that the sharp submarine ridges and deeps may not be more than one-third or two-thirds compensated.”
COMPARISON OF LOADS ON CONTINENTAL AND OCEANIC SECTORS; STRENGTH OF THE LITHOSPHERE The maps of deflection residuals and gravity anomalies, on which Barr ell based his reasoning about the dimensions of the uncompensated loads in the United States, exagger ated the dimensions of the anomalous belts. Nevertheless, it is of interest to confront his estimate of spans and intensi ties of maximum load under the surface of the continental region with his estimate of spans and intensities of maximum load in an oceanic sector.12 In the American area he recog nized two orders for the spans, “mean” and “large.” The corresponding wave-lengths and amplitudes (expressed in meters of rock), read from the maps, were assigned the values given in Table 67, which also states the figures for the Pacific region. T able 67 BARRELL’S DATA FOR COMPARING CONTINENTAL AND SUB-OCEANIC LOADS
Region Wave-length Amplitude (kilometers) (meters of rock) United States, “large” wave-length 2,800 380 United States, “mean” wave-length 600 1,015 Pacific Ocean 400 4,000
Since 1915, the date of Barrell’s paper, investigation has shown that peninsular India, rather than the United States, should be preferred as the continental region of greatest, demonstrated departure from isostasy and corresponding load on the lithosphere. For oceanic areas an analogous maximum may be sought, as Barrell suggested, among the deeps and along the Hawaiian chain. Strength of the Earth-Shells 381 It is practically impossible to calculate exactly the maxi mum stress-difference in the Indian segment of the litho sphere, the asthenosphere being supposed to have no strength. An upper limit could be found if the Hidden Range and the two adjoining troughs should represent load ing of the harmonic type discussed by Jeffreys (see p. 354). In this case the maximum stress-difference is gDHL/irh. To apply the formula it is necessary to estimate the effective ranges of anomaly in each of the three belts. For the north- T able 68 DATA FOR ESTIMATING LOADS IN PENINSULAR INDIA
Approximate Actual range of Approximate effective Region minimum span anomalies range of anomalies (km) (milligals) (milligals)
Hayford anomalies, based on Helmert spheroid Northern trough 400 +65 to —85 0 to —20 Hidden Range 600 -2 0 to +60 0 to +15 Southern trough 1,000 +5 to —75 0 to —30
Normal-warp anomalies, based on Survey of India II spheroid Northern trough 400 +80 to -70 Oto -10 Hidden Range 800 -1 0 to +70 0 to +30 Southern trough 800 + 15 to —65 0 to -2 0 (?) ern trough this has been done by assuming that the trough extends from a point northeast of Calcutta (north latitude 24° and east longitude 92°) to Peshawar (north latitude 34° and east longitude 71°). The ranges of anomaly in the Hid den Range and southern trough have been estimated from Glennie’s contour maps, charts X and XII of the Geodetic Report of the Survey of India for 1937 (in this book, Figures 50 and 51). Respectively, these charts give Hayford anom alies, based on Helmert’s 1901 spheroid, and the crust-warp anomalies, based on the Survey of India II spheroid. (See Table 68.) 382 Strength of the Earth-Shells The Hayford-anomaly map (Figure 50) gives H the aver age value of about 200 meters and L the value of about 1,300 kilometers. With g at 980 dynes, D at 2.67, and h at 60 kilometers, the maximum stress-difference would be approxi mately 400 kilograms per square centimeter. If the conditions of the map of “normal crust-warp” anomalies be assumed, the maximum stress-difference would be somewhat smaller.
T able 69 DATA FOR ESTIMATING LOADS IN OCEANIC AREAS
Approximate Region minimum Approximate range of anomalies (milligals; span (km) International spheroid) Free-air anomalies Hayford anomrlies Mindanao Deep 200+ -198 to +270 +21 to +134 Hawaii (Mauna Kea profile) 400 +657 (Mauna Kea) + 188 (Mauna Kea) Hawaii (Honolulu pro- file) 400 -9 6 to +213 — 2 to +50 Banda Sea 550 -102 to +193 +6 to +101 Gulf of Mexico 700 —88 to +37 - 3 to +70
According to Glennie, one foot of rise for the geoid corre sponds to two milligals of anomaly.13 If this rule be ap plied to the compensated geoid, based on the Survey of India II spheroid, the range of intensities of the positive and nega tive loads comes out at almost the same value as that found directly from the anomaly map, while the spans of the loads are little changed. Hence geoid and anomaly pattern es sentially agree in the data from which maximum stress- difference can be estimated. The calculated values of stress-difference are decidedly rough, because the Indian “wave” of abnormality is not symmetrical or regular in the sense of the Jeffreys harmonic. Still more important is the fact that the Hidden Range and two troughs are not parts of world-circling loads of the har Strength of the Earth-Shells 383 monic kind. Actually each is an anomalous area limited in length as well as in width. Hence it seems clear that the maximum stress-difference is much smaller than any of the quantities just derived. Table 69 bears values of anomaly in specially important marine areas. Let us estimate the corresponding loads on the lithosphere, first on the assumption that they can be de rived from the free-air anomalies. Since we do not know the amount of the (regional) isostatic compensation, the estimated loads will be greater than the actual loads—per haps 50 per cent greater. The Mindanao Deep represents the middle member of a greatly elongated, triple inequality with wave-length of about 350 kilometers. From east to west the free-air anom alies (Vening Meinesz stations 143 to 146) read: +46, +48, — 198, and +270 milligals. The lithospheric load would thus approximate to a harmonic with half-amplitude of 1,700 meters of average surface rock. Assuming this value and 350 kilometers for L, the Jeffreys formula gives a maxi mum stress-difference not far from 700 kilograms per square centimeter. A similar computation for the profile across the great Hawaiian pile of lava at Honolulu (Vening Meinesz stations 111 to 114, with free-air anomalies at —96, +169, +213, and —14 milligals) leads to estimated maximum stress- difference of the same order as at the Mindanao Deep. In each case the actual maximum may approach 500 kilograms per square centimeter. The foregoing estimates of intensity for continental (In dian) and sub-oceanic loads are exceedingly crude, but they seem to corroborate Barrell’s judgment that the sub-Pacific part of the lithosphere is considerably stronger than—per haps twice as strong as—the continental part. In no case does the estimate of stress-difference seem to demand an in credible strength for the lithosphere, especially in view of 384 Strength of the Earth-Shells the probability that high pressure increases the strength more than temperature lowers it.
EXPERIMENTS ON THE RELATION OF HIGH CONFINING PRESSURE TO THE STRENGTH OF ROCK Manifestly any valid conclusion regarding the strength of the lithosphere should be found to agree with laboratory ex periments designed to show how the strength of crystallized rock is affected by high confining pressure, applied at ele vated temperature. Unfortunately, adequate experiments of the kind are not easily made. Those of Adams and King seemed to prove a fourfold increase of the strength of granite when exposed to the pressure and temperature ruling at the depth of about 17 kilometers below the earth’s surface, but the method of study did not permit an exact result.14 By a different and better method, Griggs has shown that the ‘ 'ultimate” strength (see p. 8) of Solenhofen limestone, at room temperature and under a confining pressure of 10,000 atmospheres, is about five times as great as at one atmos phere. Again at room temperature, he found that this limestone, unconfined and subjected for 550 days to a uni lateral pressure of 1,400 kilograms per square centimeter (normal strength at 2,560 kilograms), kept flowing (creep ing) at a rapidly decreasing rate. Yet, even under these comparatively simple conditions, the fundamental strength could not be determined. He found the elastic limit of the limestone to be raised only ten per cent by a confining pres sure of 10,000 atmospheres. Griggs has begun to study the effects of pressure and temperature on the rate of elastic flow (elastic afterworking) and “pseudoviscous” flow of rock un der stress, and it is hoped that he will get results bearing on the relations of the two variables to “fundamental” strength.15 Particularly intriguing is his discovery (unpub lished experiments) that, in the presence of water, granite at Strength of the Earth-Shells 385 400°C., under confining pressure of 1,000 metric atmospheres and under unilateral compressive stress of 500 atmospheres, showed measurable flow, which continued for many days. Analogous experiments showed that even quartz in the pres ence of water becomes plastic. These discoveries show that a long and complicated series of tests are needed to determine the fundamental strength of the rocks composing the litho sphere. If the deeper and greater part of this shell is dry, the laboratory results already published would seem to per mit belief that the mean strength of the lithosphere is at least twice that of good granite in the quarry.
THE UNSTABLE GLACIATED TRACTS Some of the most impressive areas of one-sign anomaly are regions characterized by strong earthquakes, which may in dicate a step-by-step diminution of the respective abnormali ties in gravity. Possible examples include the Pamirs, the Gangetic basin, Burma, Japan, parts of the East Indian and West Indian archipelagoes, Tonga, California, and the mid- Atlantic Swell. Without knowledge of the amounts by which the recorded anomalies exceed the anomalies which would obtain if each region were stabilized, it is unsafe to at tempt to calculate the intensity and distribution of the stresses involved, especially the maximum stress that would match the strength of lithosphere or asthenosphere. When we also remember how limited are the areas adequately sown with gravity stations, and how difficult is the translation of regional anomaly into actual uncompensated loads on the earth’s body, it becomes clear that few fields can furnish the information required for the solution of the problem of ter restrial strength. Among all the regions dominated by anomalies of one sign, two, the glaciated tracts of northeast ern North America and northwestern Europe, are truly illuminating. We shall now turn to their consideration. As stated in chapter 10, the post-Glacial upwarpings of 386 Strength of the Earth-Shells the lithosphere in these two regions, and also in ten other tracts where great masses of Pleistocene ice have been melted away, are best regarded as the effects of isostatic adjustment. Every other published explanation has practically no war rant from the facts of geology and is highly unsatisfactory. In fact most geologists and not a few geophysicists believe it to be a matter of common sense to accept the isostatic ex planation. If this judgment is sound, it gives a premise from which a maximum value for the strength of the astheno- sphere at a given level within it may be rather closely esti mated. The data needed for such estimates refer chiefly to Fen- noscandia, but there is no reason to suppose that the astheno- sphere under that broad area has properties essentially dif ferent from those of the asthenosphere under other broad continental regions. The isostatic theory demands that in average the gravity anomalies over Fennoscandia should be negative, and should be increasingly negative along radii drawn from near the terminal moraine to the locus of great est thickness for the vanished icecap. These deductions are in accord with the facts of the anom aly map of Finland, where the mean anomaly (based on the Heiskanen triaxial spheroid of 1938) at the central locus is between —20 and —30 milligals.* Hirvonen’s map or the map of Figure 77 covers no more than about 30 per cent of the region inside the zero line for contemporary uplift, but the maps of isobases for former and present-day warping within the glaciated tract as a whole strongly suggest that quantitatively Finland furnishes a good sample of the be havior of the entire tract. The anomaly at the locus of maximum loading represents a defect of mass equal to a plate of granite with thickness of * The “locus” here meant is assumed to be the area extending about 100 miles from the line where the ice-load was at maximum. In this area 17 stations were situated, and it is thought that the mean of the 17 anomalies is likely to give the best available value for the central anomaly. Strength of the Earth-Shells 387 180 to 270 meters. Each thickness is of the same order as the 210 meters which Niskanen finds to be the amount of future upheaval needed to produce equilibrium. He de duced this value from the measured rates of uplift at certain epochs during the last 8,700 years. He thinks that his
F igure 84. Niskanen’s map showing with contour lines (interval 20 meters) the amount of warping still needed to restore isostatic equilibrium. method of calculation gives a result more reliable than that based on the anomaly map.16 Figure 84 is a copy of Nis kanen’s map of contour-lines showing the amount of future uplift from point to point in Fennoscandia if crustal equilib rium be finally established. The defect of mass decreases outwardly in all directions, 388 Strength of the Earth-Shells becoming zero at or near the hinge-line of contemporary warping. If, then, the uplift is isostatic, the stress in the asthenosphere is above the strength of this shell, and the stress can be estimated to a fair degree of approximation. The stress at any level in the asthenosphere can be com puted by formulas analogous to those developed for har monic loads by Darwin and Jeffreys. The results would not
H
F igure 85. Stress diagram for the case of a semi-ellipsoidal load on a semi-infinite solid (after Timoshenko). be greatly different from those found when the negative load on the Fennoscandian sector is assumed to be distributed in the form of a semi-ellipsoid. * Timoshenko illustrates the case * A. Penck {Sitzungsber. Akad. Wissen., Berlin, vol. 22, 1922, p. 308) described the surface form of the icecap as near that of a paraboloid, which is not essentially different from a semi-ellipsoid, so far as the present problem is concerned. Strength oe the Earth-Shells 389 for a positive load of this kind, pressing on a semi-infinite, elastic solid of uniform properties. Figure 85 is a copy of his diagram and portrays the results of actual calculation. Therein the line HO is the direction of maximum pressure on the semi-infinite solid; r is the radius of the load at the inter face; P is the pressure at the point O. The lengths of the barbed, vertical lines vary with the intensity of the pressure at the respective points on the interface. In the semi infinite solid the maximum shearing-stress is 30 per cent of P and occurs under O and at a depth of about 0.78r from the interface, where the stress is zero.17 The pressure exerted by a column of granite 180 meters high is about 50 kilograms per square centimeter. The Timoshenko diagram implies that the maximum shearing- stress at the depth of 100 kilometers under the center of the Fennoscandian tract is not far from 4 kilograms per square centimeter. It would be about 6 metric atmospheres, if the central-area anomaly be —30 milligals. Since the upwarp- ing continues, the indicated strength of the asthenosphere (equal to twice maximum shearing-stress supported) at the 100-kilometer level is no more than 8 to 12 kilograms, and at the top of the layer no more than 5 to 8 kilograms. If the upheaval should continue at the present rate for another 10,000 years, the indicated maximum would be halved in each case. In any case we have arrived at a degree of strength which is at least two orders of magnitude smaller than the value estimated by either Barrell or Jeffreys. And there is no apparent necessity of excluding the possibility of effectively-zero strength.* * From the rates of upwarping in Fennoscandia, estimates of the mean viscosity of the earth’s silicate shell have been made. In their calculations of this quantity, N. A. Haskell (Amer. Jour. Science, vol. 33, 1937, p. 22), F. A. Vening Meinesz (Proc. kon. Akad. Welen., Amsterdam, vol. 40, 1937, p. 654), and E. Niskanen (Annales Acad. Scientiarinm Fennicae, ser. A, tom. 53, No. 10, 1939) assumed 1,200 or more kilometers for the thickness of the yielding layer. Respectively, they found the mean viscosity to be 2.9 X 1021, 9 X 1021, and 1.1 X 1022 poises. R. van Bemmelen and P. Berlage (Gerlands Beitr. zur. Geophysik, vol. 43, 1934, 390 Strength of the Earth-Shells
COMPARISON OF CONDITIONS IN INDIA AND FENNOSCANDIA In Fennoscandia, “Nature’s experiment” with a tempo rary glacial load has provided a way of estimating the upper limit to the strength of the asthenosphere. India is part of an enormous and apparently stable field of dominantly one- sign (negative) anomaly, when the individual anomalies are based on the International formula. If this Asiatic field be assumed to represent a real negative load, and if the corre sponding stress in the asthenosphere be calculated by the method of Darwin or Jeffreys, a minimum strength for the shell is indicated. This minimum strength is many times greater than the maximum strength deduced in the glaciated tract. However, geologists know of no cause for any great differ ence in the elastic competence of the two earth-sectors. Hence the contrast of the two estimates of asthenospheric strength leads us once more to examine the validity of the International formula.* When all the reductions are based p. 19) assumed a thickness of 100 kilometers for the asthenosphere and obtained a lower value—1.3 X 1020 poises—for the mean viscosity. All those estimates were made on the premise that the lithosphere offers no special resistance to the upwarping. Yet it is a question whether this assumption is justified. To what extent is the rale of upheaval determined by the “pseudo- viscosity” (Griggs) of the lithosphere? According to W. Schweydar (Verojjent. preuss. Geodat. Inst., N.F., No. 54, 1912, and No. 79, 1919), the viscosity of the asthenosphere, if 400 kilometers thick, need be no more than about 1012 poises to permit the existence of the fortnightly body-tide of the earth. If the thickness is 100 kilometers, its viscosity need be no more than 109 poises. That the pressure on the asthenosphere, with minimum of about 17,000 atmospheres, should raise the viscosity of molten, “ultra-basic” basalt from its one-atmosphere value of about 103 poises to 109 or even 1012 poises seems not at all incredible. If the asthenospheric viscosity has either of these comparatively low values, we can understand why there are no physiographic signs of a belt of notably super-elevated ground outside the zero isobase. We can also understand why the Lithuanian plain, situated in the peripheral belt around the glaciated tract, has not a positive Hayford anomaly of gravity (see Table 31). Similarly we can account for the horizontality of the old beaches outside the Whittlesey and Al gonquin hinge-zones of the glaciated tract in North America. * The writer has already briefly discussed this subject (Bull. Geol. Soc. America, vol. 50, 1939, p. 387). Strength of the Earth-Shells 391 on this formula, both regions are found to have comparable negative mean anomalies and comparable negative maxi mum anomalies. Each of the two areas has a minimum span of at least 1,200 kilometers. If the asthenosphere is no stronger under India than under Fennoscandia, we may well ask why the upward pressure matching the assumed anomaly fields bends up the Fennoscandian segment of the lithosphere, and fails to bend up the Arabian Sea-India seg ment. The question is all the more serious because, by the assumed mode of reduction, the Asiatic field is actually the broader and therefore structurally less able to resist the pressure. The problem becomes much less formidable when the re spective fields of anomaly are disclosed after reductions based on the Heiskanen triaxial formula for the figure of the earth are made. This change in the basis of reduction somewhat increases the dimensions of the negative Fenno scandian field, but breaks up the negative field of India into three parts—the middle part, Hidden Range, being decidedly positive. (See chapter 8, section on conditions in India.) Stability for the lithosphere along the middle, positive belt is favored not only by the flexural strength of this earth-shell, but also by the comparative narrowness of the belt, by “supporting pillars,” and probably to some extent by the curvature of the shell.18 Stability for each negative trough is favored by the strength of the lithosphere and by limitation of span of the load; by local “sinkers,” correspond ing to included positive areas of anomaly; and by the down ward component of pressure elastically transferred from the middle belt of excess, positive load. There may be an additional reason why India has long escaped isostatic adjustment. The recent deformation of the young sedimentary beds of northern India is of the kind expected if, since the Himalayan revolution, the whole peninsula has been horizontally compressed, across the axes 392 Strength of the Earth-Shells of the three belts of anomaly. It is conceivable that the horizontal pressure here increases the strength of the litho sphere. On the other hand, neither Fennoscandia nor east ern Canada shows any sign of being similarly affected by abnormal horizontal compression. How can the stability of the broad southern area in penin sular India, characterized by negative anomaly, be reconciled with the instability of the negative Fennoscandian area? The southern area of India is to be emphasized, because the span of its uncompensated load is larger than the span of the other negative area—that underlying the Ganges plain. There are two reasons for the contrast of behavior. First, we note that the stiffness of a loaded plate, other conditions being equal, varies inversely with the fourth power of the radius of the plate.* Also important are the distributions of the (negative) loads in the two regions. Figure 84 shows the unbalanced load to be greatest at the center of the Fennoscandian glaciated tract (former positive load) and diminishes to the zero isobase with fair regularity. In contrast, Figure 51 indicates that the maximum intensi ties of the (negative) load in southern India are not at the center of the negative area, but are located well out toward the periphery of this area. Assuming equal thicknesses of the lithosphere, and equal strengths of the lithosphere, in the two regions, it appears, after rough computation, that the up warping tendency in Fennoscandia is at least 25 times as great as the upwarping tendency in India.19 This con clusion has been drawn on the assumption that there is no systematic error in the published Indian anomalies. The anomalies were actually computed after supposing that the force of gravity at the base station, Dehra Dun, is 979.063 gals. However, the Survey of India is now con
* By error it was stated in the writer’s paper, published in the Bulletin of the Geological Society of America (vol. 50, 1939, p. 408), that the second, rather than the fourth, power is here involved. Strength of the Earth-Shells 393 vinced that the force at this point is greater. Heiskanen, relying on Hirvonen’s recent discussion of the relevant data, is of opinion that g at Dehra Dun is better estimated at 979.078.20 If that be a correct judgment, about +15 milli- gals should be added to each anomaly, and the region of southern India now under discussion should everywhere be about 15 milligals less negative than appears from the pub lished tables. The indicated span of the negative load in southern India would be diminished, and the average indi cated intensity of the load would be diminished by nearly one half. The upwarping of Fennoscandia will continue until, with further isostatic adjustment, its negative load becomes les sened so as to be, like the load in southern India, within the flexural strength of the lithosphere. If the maximum stress- difference in the lithosphere under southern India is at the strength (it may, of course, be below the strength), Fenno scandia will probably cease to rise when the negative anom aly at the center is about half a milligal. An anomaly of this size means a maximum (negative) weight of four or five meters of granite. Is it not possible that the continental part of the lithosphere can, unaided, bear a lenticular load whose intensity decreases from half an atmosphere at the center to zero at the radial distance of 600 kilometers? It goes without saying that all these deductions and queries relating to Fennoscandia will need revision after the whole area has been sufficiently covered with gravity sta tions, and also after the glaciated tract of eastern Canada has been gravitationally explored with thoroughness.
HORIZONTAL VARIATION OF THICKNESS OF- THE LITHOSPHERE Sialic rock is a better conductor of heat than simatic rock, but is a more efficient furnace because of radioactivity. With proper allowance for the corresponding effects on rock 394 Strength of the Earth-Shells temperature, it seems reasonable to assume a thermal gradi ent steeper under the continents than under the oceans. If, then, the gradient in all sectors is steep enough to keep the asthenosphere in the vitreous state, the lithosphere, now visualized as a true crust, must be thicker under the ocean than under a continent. Figure 9 indicates respective, merely estimated, thicknesses of about 77 and 60 kilometers. Thicknesses one sixth greater in each case may be nearer the truth. The continental part of a crust with the properties ex pected from such an earth-model should itself have variable thickness, depending on the thickness of the more radioactive sial and on the amount and recency of major stoping. If, as suggested elsewhere, a batholith is the upper part of a huge magmatic body merging directly into the vitreous astheno sphere, the thickness of the solid roof of the batholith would also be the local thickness of the lithosphere.21 The thick ness increases as the batholith cools and crystallizes— a proc ess involving many millions of years. Hence it is possible that the solid roofs of some Tertiary batholiths now measure far less than 60 kilometers in thickness. This theoretical deduction suggests an apparently good explanation of the recent upwarping in the Lake Bonneville region. There is no reason to doubt Gilbert’s conclusion that the systematic tilting of the Bonneville beaches repre sents a case of isostatic adjustment for removal of a load of water by evaporation and down-cutting of the outlet of the lake.* The span of this negative load was only 250 kilo meters, and its maximum intensity was no more than the weight of about 100 meters of granite (with a corresponding gravity anomaly of little more than 10 milligals). When the load is compared with the loads stably borne by the crust under peninsular India and elsewhere, we are led to suspect the yielding crust under Utah to have been abnor * G. K. Gilbert, Monograph 1, U.S. Geol. Survey, 1890. Strength of the Earth-Shells 395 mally thin. Is it possible to find a better interpretation of the facts than one assuming a broad, still hot and perhaps largely molten, batholith under the site of the late-Glacial Lake Bonneville? Special gravimetric work in the region may help to answer that question. Until that is done, we may well ponder the meaning of one of Hayford’s results from his study of deflec tions of the vertical. From all observations in the United States, he found the most probable depth of compensation to be 122 kilometers, but from the observations in his group 8, including those made in parts of Utah, Nevada, and Cali fornia, the most probable depth was estimated at only 66 kilometers.22 The contrast of the two depths seems to war rant the hypothesis that a broad region, including the Lake Bonneville area, has a comparatively thin crust, correspond ing to the solid roof of a gigantic batholith, still partly liquid. Although Barrell did not believe the asthenosphere to be vitreous, he recognized that large-scale intrusion of magma can not fail to alter the effective thickness of the lithosphere and the effective depth of compensation. He wrote: Intrusions of magma and the heat which must accompany them have set apart the Cordilleran province [of the United States] from the regions of geologic quiet, and may have decreased the densities in the outer crust sufficiently to account for the recent regional elevation above its own former level and the present level of other portions of the continent. The intra-continental compensation may therefore be of a different nature and devel oped at a higher level than the compensation which separates continents from oceans.23 It may also be asked whether the large negative anomalies within an area near Seattle can be explained by the gravita tional effect of a hot and expanded, if not liquid, batholith under the area. Let us apply these considerations to our main problem. If the lithosphere is a true crust, varying in thickness from 396 Strength of the Earth-Shells oceanic segment to continental segment, and, if the thickness varies also from region to region within each of these seg ments, the strength of the crust varies still more. Other things being equal, the maximum possible stress in a loaded plate increases with the square of the plate’s thickness. But a thin crust is, by hypothesis, hotter than a thick crust, and therefore can not permanently bear as large a stress- difference as the former could bear if it had the mean tem perature of the thicker crust. Since the sub-oceanic crust is largely or wholly simatic and therefore is provided with less heat of radioactivity than that produced in the conti nental sectors, the crust, when at thermal equilibrium, should have maximum thickness beneath the ocean. Thus we can understand why the greatest of all uncompensated but apparently supportable loads are found in oceanic re gions. If the crust under Utah was, in late-Glacial time, specially thin, we can see why it was so mobile.
STRENGTH OF THE LITHOSPHERE AT EARLIER GEOLOGICAL EPOCHS In all probability an accurate model of the earth-shells in their present condition fails to represent the shells of former eras. These can hardly be pictured without our having pre liminary answers to a number of questions, all of which are highly elusive. How was the earth originally organized? Kelvin pictured the early stages in the thermal history, on the assumption that the silicate mantle of the infant planet was a super heated, “ultra-basic” liquid of approximately homogeneous composition. With rapid radiation of heat at the surface, a thin, discontinuous crust was crystallized. Because of ex cess density the crust-flakes foundered in the remaining liquid, where they were re-melted. Repeated crustings and founderings rapidly chilled the silicate mantle until its lower part became permanently crystallized, pressure-solid. This Strength of the Earth-Shells 397 gigantic stirring, a kind of solid-liquid convection, accom panied by many re-meltings, could hardly fail to cause gravi tational differentiation of the liquid. If thereby a superfi cial, sialic layer (with relatively low density even when crys tallized) was developed, general stoping of the crust would be arrested, and this crust, overlying a residual, non-crystal- lized layer, would thenceforth be stable. The thickening of crust and crystallized mesospheric shell (see p. 13) would be slowed down, but probably not stopped, by the radio activity-of the shells. In principle, a similar result would be expected if the silicate mantle of the young earth were rapidly chilled by thermal convection without crusting. Here, also, let us make the simplifying but extreme assumption of chemical homogeneity for the 2,900-kilometer shell. At and near the surface the pressures were low and the viscosity correspond ingly low; hence there convection was rapid. Suppose that the layer thus rapidly chilled began, as a whole, to dive con- vectively through the hotter, deeper liquid. Reaching levels of greater pressure, the sinking mass of liquid would begin to crystallize. With crystallization the density of the mass increases, and the rate of sinking is accelerated. This pres sure-solid rock would come to rest on the iron core at the bot tom of the silicate mantle. Because of the slowness of thermal conduction, the sunken, solid mass is several thou sands of degrees cooler than the liquid displaced at the deep level. This little-chilled liquid is pushed up by the sunken mass, which is soon joined by an indefinite number of simi larly foundered masses. The more fusible constituents of those masses are re melted and, in the form of new liquid fractions, necessarily less dense than the original liquid, stream up toward the sur face of the globe. In this way the original liquid becomes differentiated by gravity, and the thermal convection ceases when the superficial layer approaches or reaches a sialic 398 Strength of the Earth-Shells composition. Between this layer, soon to become an un- sinkable crust, and the pressure-solid mesospheric shell, there remains a vitreous, somewhat superheated layer, whose cooling must be slow, especially in the presence of radio activity. According to either of the two speculations regarding the march of events, a vitreous asthenosphere was established soon after the earth began its life as a separate body. The slow thickening of the lithosphere tended to make it stronger. However, it is conceivable that this tendency has been tem porarily and regionally offset to some extent by primeval convective movements in the asthenosphere, and also modi fied by differential radioactivity in the earth sectors. More over, the internal temperature must be altered by the devel opment of mountain roots (with extra radioactivity) and by the stoping localized under mountain chains. Hence we may well ponder another question: how important has been this orogenic chilling (and subsequent radioactive heating by mountain roots) in changing the thicknesses of the litho sphere and asthenosphere and the strength of the litho sphere? Without enlarging on these problems, where speculation is so little controlled by ascertained facts, it seems clear that geologists should consider the probability of secular changes in the general thickness, and epochal changes in the local thickness, of the lithosphere. Such changes would be asso ciated with increases or decreases of the lithospheric strength, and these may be supposed to have influenced the tempo and scale of diastrophic processes during past eras. THE ASTHENOSPHERE AND THEORIES OF DIASTROPHISM AND PETROGENESIS Any theory that makes thermal convection the ruling con dition for the making of mountain chains or mediterranean sea-basins implies extreme weakness for the asthenosphere. Strength of the Earth-Shells 399 The same implication attaches to the crust-warping hypothe ses of Glennie and Vening Meinesz. More explicit is the direct testimony from geodetic tests of isostasy and from the contemporary warping of glaciated Fennoscandia and east ern Canada. Dynamical geology furnishes two other con firming facts. In the first place, we note that each major orogenic revolu tion was accompanied by extended, horizontal shearing of all, or a large part of, a superficial earth-shell over the under lying shell. Such horizontal displacement seems possible only if the lower layer has a minimal power to resist shearing- stress. Moreover, the observed tectonics show that the superficial shell, transmitting the orogenic thrusts, is rela tively thin. The upper part of the displaced sial is visibly sliced by low-angle thrust-faults, but the migration of the driving lithospheric segments means that most of the dis placed shell lies far below the observable horizons. The in terface where the rock becomes weak enough for the princi pal horizontal shearing must lie still deeper, and, from con siderations regarding the thermal gradient, this depth is necessarily placed at a level several tens of kilometers below the surface. Thus the zone of easy horizontal shearing be gins at a depth of the same order as that assigned to the top of an asthenosphere, detected by studies of isostasy. Secondly, the existence of a liquid or approximately liquid asthenosphere is strongly suggested by the countless facts of igneous geology. The hypothesis that the lithosphere is crystalline, a few scores of kilometers in maximum thickness, and everywhere underlain by a hot, vitreous substratum pro vides what appears to be the best working theory of the chemical nature of magmas and of their modes of eruption. Among the observed facts leading to that fundamental hy pothesis of change of state in depth are: measured thermal gradients and the possibilities of their interpretation; the prevailing sequence of igneous rocks, considered in terms of 400 Strength of the Earth-Shells chemical composition as well as order of eruption; and the wide basining of the floors of plateau-basalts. In general no petrogenetic theory that does not recognize a specific, world- circling asthenosphere of this kind has been found to explain so many facts of the field. The crust-substratum theory it self has not been demonstrated, but nevertheless its unique power to account for the facts is suggestive when the strength of the asthenosphere is in question. For it is hardly to be doubted that a rock layer, too hot to crystallize, has only a minute strength or no strength whatever.* THE ASTHENOSPHERE AND DEEP-FOCUS EARTHQUAKES A considerable percentage of all world-shaking earth quakes have foci ranging from 70 to 700 kilometers. A typ ical shock of the kind is due to the release of elastic energy comparable with that releasing a normal earthquake with focus between 10 and 40 kilometers from the earth’s surface. A large part of the energy of a deep-focus shock is carried by the transverse, S, or shake wave. Some geophysicists are therefore of opinion that an asthenosphere with strength approximating zero can not begin at any depth smaller than about 700 kilometers. For example, Jeffreys deduces, from the reality of deep- focus shocks, a strength of about 1,000 kilograms per square centimeter for the material reaching down to the 700-kilo meter level at least. This is about the strength of good granite in the testing-machine. To reconcile that conclusion with the demonstrated degree of isostatic equilibrium, Jeffreys suggests that isostasy is a highly exceptional condition of the earth. He assumes the condition to have been established during major orogenic * The crust-substratum theory has been discussed in detail in the writer’s books “Igneous Rocks and the Depths of the Earth” (New York, 1933) and “Architec ture of the Earth” (New York, 1938). Strength of the Earth-Shells 401 disturbances, and preserved for only a relatively short time after each paroxysm of mountain-making. He writes: The formation of a mountain chain represents a shortening of the earth’s crust by something like 40 kilometers, possibly rather more. A general state of stress is needed to produce this, and its first stage would be a fracture or some other type of failure of elasticity extending right through the crust. We can suppose the stress enough to overcome the strength at this stage; a stress that could be relieved only by a displacement of 40 kilometers would be enough to overcome the full strength of the crust. This, however, is not the end of the matter. A simple fracture would leave such inequalities of height that gravity would pro duce further fractures, and a complicated set of local movements would ensue before equilibrium could again be reached. This mechanism provides an explanation of the nappe structure ob served in the Alps and other great mountain systems. But it does not follow that the strength below a mountain chain after this extensive fracturing is as great as before; a cracked cup is not as strong as a new one. A much smaller strength in the lower layer may be available to oppose fresh adjustments. Thus we should be entitled to regard the 6 X 107 dynes/ cm2 derived from the imperfections of isostasy as the strength of the lower layer when broken, not as the strength when entire. The apparent inconsistency between isostasy and the other lines of evidence may therefore disappear when we recognize that they refer to two different stages of fracture; one refers to the fracture of new ma terial, the other to the stress-difference needed to produce sliding on planes of fracture that already exist.24 Thus, for example, it is supposed that the complex frac turing, a kind of coarse brecciation, of the lithosphere during the mid-Tertiary orogeny led to approximate isostasy, which, because of the recency of the paroxysm, still exists. This explanation might be conceived for the Alpine zones, but it does not account for the isostatic condition of the vastly greater areas far from the belts of mountain-building. Ac cording to the contraction theory, the horizontal force that crumpled the Tertiary geosynclinal prisms was propagated along the curved lithosphere outside these prisms. Transfer 402 Strength of the Earth-Shells of pressure would be difficult, if not impossible, if the extra- alpine segments of the lithosphere were thoroughly fractured. Hence the great shields could not be isostatically adjusted, and yet, by hypothesis, secular erosion must have thrown those wide regions out of balance. Nor would distant oceanic belts, which for similarly prolonged periods had been loaded with sediments, be restored to isostasy. It therefore appears that Jeffreys’ suggestion does not satis factorily reconcile the world-wide rule of isostasy with the idea of an asthenosphere with granite-like strength. The hypothesis faces other weighty objections. First, it may well be doubted that thermal contraction would lead to sufficiently widespread fracturing, brecciation, of the thick layer below the visible lithosphere. Secondly, even if gen eral brecciation under a mountain chain were to take place, it is hardly conceivable that the strength of the deep shell would remain small for more than a moment of geological time. Under the high pressure the fractures would be speed ily healed, with restoration of the original strength. This opinion is justified by the observed behavior of the materials which, under the pressure of 20,000 to 50,000 atmospheres, were sheared by Bridgman to the point of rupture. Almost instantaneous “self-welding” was the rule.25 In the third place, the hypothesis provides no good explanation for the prolonged yielding of geosynclinal floors during the slow thickening of the sediments on those floors. Again, the hy pothesis disagrees with the evidence of exceedingly low strength for the asthenosphere under the glaciated tracts.
Jeffreys’ hypothesis is based on an unproved assumption— that an asthenosphere with extremely small strength could not accumulate enough elastic energy to permit sudden dis placement and strong shock at any interface within the Strength of the Earth-Shells 403 layer. This is the essential problem. If the asthenosphere has vanishingly small strength but finite viscosity, great shear-energy can be developed in the shell only by a com paratively rapid concentration of shearing-stress. Jeffreys deduced great strength for the asthenosphere because “no cause of a sudden increase of stress at an internal point has been suggested.”26 Yet, in view of the combined geodetic and geological evidences for extreme weakness of the as thenosphere, it seems right to believe that there must be some cause or causes for just such sudden increase of stress in this layer. With existing information any suggestion of cause can not be other than speculative, but it is also true that the meaning of deep-focus earthquakes will never be assured until all speculative possibilities have been criti cally examined.* One possibility seemed to be in sight after Bridgman re ported on the behavior of solids when exposed to unilateral pressure of 20,000 to 40,000 atmospheres and a simultaneous twist at right angles to that axis of pressure. In general, each material was made to flow by the external, torsional stress, but the flow was interrupted by sudden fracture and slip. Clearly, in these many instances the solids became charged with internal stress in shear—a stress ultimately be coming intense enough to compel sudden fracture and shock. The interruption of the flow by the jerking scissions, con tinuing periodically as long as the twisting force was applied, was illustrated with crystals, crystalline aggregates, powders, and amorphous substances including cold glass, j However, * B. Gutenberg’s recently expressed conclusion (“Internal Constitution of the Earth,” New York: McGraw-Hill Book Company, Inc., 1939, p. 298) may be noted: “There is no evidence of a special causative mechanism for the production of deep shocks; the forces acting appear to be identical with those which occasion earthquakes at normal depth. Whereas at normal depths the accumulation of strain is made possible by the strength of the rocks, at the greater depths the high coefficient of viscosity is sufficient, and no conclusion as to strength can be drawn.” (Reprinted by permission of the publishers.) See also B. Gutenberg and C. F. Richter, Bull. Geol. Soc. America, vol. 49, 1938, p. 285. t P. W. Bridgman, Proc. Amer. Acad. Arts and Sciences, vol. 71, 1936, p. 387; 404 Strength of the Earth-Shells a sample of pitch (at room temperature; a classic type of elastico-viscous matter) failed to show such storage and quick release of shearing-stress. In this case the limit of the pressure was only 20,000 atmospheres, but it seems likely that the same negative result would have been found at pres sure twice as great. Thus the Bridgman experiments here referred to do not give an assured explanation of deep-focus earthquakes, if these are due to sudden scissions in a purely elastico-viscous asthenosphere. Further, it would be unsafe to assume difference of behavior if the asthenosphere has a finite but minute strength. And we note that the torque in most of Bridgman’s experiments was applied with rapidity on material of enormous viscosity, while we have no right to assume our asthenosphere to have anything like the same viscosity. Solution of the deep-focus problem demands knowledge of the state of matter in much, if not all, of the earth’s silicate mantle. Such knowledge is beyond contemporary science. To make any progress with the present question, we can not avoid pyramiding speculative ideas. The writer has done just this. Prompted by the facts of structural and dynam ical geology, he has postulated a dominantly elastico-viscous, vitreous asthenosphere, beginning at the depth of 60 to 80 kilometers. Such a liquid or quasi-liquid layer, like the overlying, strong lithosphere, must have limited thickness, if the earth has a roughly triaxial figure. For the triaxiality means stress at depths of thousands of kilometers. If the earth’s iron core is “fluid,” the stress corresponding to the triaxiality must be distributed through the greater part of the silicate mantle, the mesospheric shell. The required strength of this shell is assumed to be due to its crystallized state. The interface between it and the asthenosphere is not likely to be any deeper than the Jeffreys discontinuity at Jour. Geol., vol. 44, 1936, p. 661. On p. 662 of the second paper, Bridgman stated: “It would seem that this sort of rupture must be a factor in deep-seated earthquakes.” Strength of the Earth-Shells 405 the depth of about 480 kilometers, and may be no deeper than the 100-kilometer or 120-kilometer level. A mesospheric shell of quite moderate strength, but nearly 2,500 kilometers in thickness, could easily bear the stresses implied by the triaxial figure of the globe. The stress- differences would have to be referred to an appropriate lack of asymmetry in the mesospheric shell itself. The cause of the asymmetry will later engage attention, but the next step in our guessing will be to ask whether the suggested earth- model can be retained, in spite of the fact that the astheno- sphere is subject to sporadic, violent fracture and self generated shock. The imagined model implies the possibility of foundering of large blocks of the denser lithospheric rock if once im mersed in the vitreous shell, even if this is as “basic” as oceanite and peridotite. The argument for belief in such localized stoping, as a necessary accompaniment of moun tain-making on the grand scale, has been outlined else where. 2 7 If the reasoning is sound, it indicates one way in which the asthenosphere may become both physically and chemically heterogeneous. The down-stoped blocks are ultimately melted at great depth. After the change of state, their material, now with density lower than that of the sur rounding asthenospheric glass, ultimately shears its way up ward. It is conceivable that these displacements are rapid enough to cause sudden fractures and shocks in the astheno sphere. Does the asthenosphere become heterogeneous for a quite different reason—because of the rise of gas from the meso spheric shell, as this shell slowly thickens with the cooling of the earth? A concentration of this gas—analogous with the mass of volatiles associated with the emplacement of the visible pegmatite dike—would produce a local decrease of viscosity and a tendency toward a local, rapid increase of any shearing involved by isostatic adjustment for surface loads. 406 Strength of the Earth-Shells Again, it is worth asking whether localized shearing, how ever caused, may heat the material along an interface of shearing sufficiently to lower the viscosity at that interface to a notable extent. If this occurs, there appears a possibil ity of displacement at the interface, so accelerated as to cause a shock. Bridgman’s high-pressure experiments suggest still an other way in which deep-focus earthquakes may originate.28 He has found that polymorphic changes, caused by increase of pressure and accompanied by diminution of volume, are characteristically sudden. Is this rule important in the case of a crystalline block sinking to great depth in the vitreous asthenosphere? If the blocks do thus suddenly shrink in volume, the shears in the overlying asthenospheric glass, adjusting itself to the new condition, would also be sudden. The asthenosphere of the described earth-model is topped and bottomed by crystallized earth-shells, both charged with shearing-stresses. If either of these truly solid shells is sud denly broken by high-angle faults, the asthenosphere be comes locally and suddenly stressed. It is conceivable that relief of the new stress in this shell is begun by sudden frac ture and completed by flow. The fact that most of the recorded deep-focus shocks occur under broad belts of recent, energetic orogeny suggests one more possibility. As described in the writer’s “Architecture of the Earth,” mountain-making of the Alpine or first-rank type seems necessarily accompanied by the diving of enor mous masses of simatic, lithospheric rock into the astheno sphere. Thus the belt under the growing mountain-chain is chilled by huge, downwardly directed prongs of the litho sphere, as well as by down-stoped blocks. Such orogenic chilling of the upper part of the asthenosphere should there develop early-formed crystals, scattered through the mass. The net density of the crystal-sown part—a suspensoid— would exceed the density of the unchanged glass. Let us Strength of the Earth-Shells 407 assume this contrast of density to cause convective over turn, and that the crystal-sown mass sinks to great depth. It seems quite possible that the glass of the sunken sus- pensoid should be undercooled several hundreds of degrees, with reference to the freezing temperature at the greater depth. If so, we should expect: sudden freezing by the in creased pressure on this glass; hence sudden shrinkage of volume for the sunken two-phase mass; and therefore read justments and sudden shearing—fracture and shock—in the overlying, viscous glass. All these speculative queries, suggested by study of a par ticular earth-model, elude adequate answers, but perhaps their listing may indicate the fallacy of assuming, off-hand, that the reality of deep-focus earthquakes means great strength in the asthenosphere. This assumption is in mani fest contradiction with the results of testing isostasy, and especially with the testing in the glaciated tracts. THE ASTHENOSPHERE AND WARPED PENEPLAINS To be a good guide in research, an earth-model involving a thoroughly weak asthenosphere should withstand another test. A vital problem is the meaning of the upwarped, old- mountain peneplains, now essentially in isostatic balance with the surrounding sectors of the earth. Willis, Barrell, and others have assumed that the erosive removal of load from each mountainous sector was not accompanied by cor recting flow in depth.29 Thus, they thought the strength of the asthenosphere to be so great as to delay isostatic adjust ment for tens of millions of years. That conclusion was based on several tacit assumptions: (1) that the mountainous sector was initially in isostatic balance and not overloaded; (2) that the ultimate upwarping of the peneplained surface was not due to local, vertical expansion (attenuation) of the lithosphere; (3) that the thermal conditions under the moun tain belt and the possibility of a vitreous substratum could 408 Strength of the Earth-Shells be ignored; and (4) that the shrinkage of crystallizing mag matic bodies, injected into the mountain roots, would also be negligible. Any initial overload in an earth-sector which has just un dergone an orogenic paroxysm, and thus has been weakened, is likely to have been relatively small. The second tacit assumption is more vulnerable, because it disregards the thermal changes due to movements of the isotherms, which, during the mountain-making, were depressed and afterwards were raised by slow conduction of heat from the earth’s in terior and by specially effective radioactivity of the moun tain roots. The volume changes so induced in a vitreous asthenosphere and in magmatic intrusions would be too com plex to warrant an attempt at detailed description. It would be particularly difficult to date those underground changes of volume within the long interval between the orogenic paroxysm and the final upwarping of the surface. It seems clear, however, that all the thermal changes must have been exceedingly slow under every old-mountain pene plain, and that the suggested test of isostasy has no value until it becomes founded on a correct idea regarding the state of the asthenosphere. On the other hand, it is highly probable that some of the warped peneplains were, before upwarping, actually belts of negative load, and that at least part of each of these uplifts was due to deep flow—that is, delayed isostatic adjustment as usually understood. We have seen that isostasy has to be of regional character, the spans and amplitudes of the uncompensated loads being limited. But, within these limits, an unwarped peneplain should be tolerated by the unaided, strong lithosphere. STRENGTH OF THE MESOSPHERIC SHELL By supposing the thick mesospheric shell to be strong and asymmetric, we have found a theoretical explanation for the Strength of the Earth-Shells 409 ellipticity of the equator and of each parallel of latitude in the geoidal figure. We assume a similar departure of the surface of the shell from the shape of a rotation-spheroid, and a density for the shell higher than that of the astheno- sphere. If we accept this picture of the deep interior, we are naturally impelled to ask three questions: Why this ex cess of density? Why is the mesospheric shell strong? Why does its upper surface depart from circularity in all sections parallel to the equator? It is rational to assume the material just above and below the surface of the shell to be chemically the same. If we further suppose the shell to be crystallized by the high pres sures upon it (ranging from 150,000 or less to more than 1,000,000 atmospheres), its upper part would be something like six per cent denser than the overlying glass, and the pressure-solid rock would have some strength.* The cause of the asymmetry of the mesospheric shell repre sents a fundamental question, which can be answered only in a speculative way.f One’s thought naturally turns to the conception that the moon’s material was torn out of one hemisphere of the earth. Such a catastrophe would have produced a high degree of asymmetry with respect to both mass and temperature. The superficial healing of the wound would be rapid, but, if the pressure-solid mesospheric shell had been developed before the disruption, this ancient event might conceivably have caused a permanent inequality in the surface of that shell. { There is another possibility, based on the fact that the sial is more radioactive than the sima. While the heat of radio * J. Barrell (Jour. Geol., vol. 23, 1915, p. 331) was led to ascribe to his "centro- sphere” strength much surpassing that of the asthenosphere; and G. K. Gilbert (Prof. Paper 85c of the United States Geological Survey, 1913, p. 35) suggested that areas of one-sign anomaly may be in part explained by the gravitational effects of abnormal masses in the “centrosphere.” fThe writer has touched on this subject in two recent papers: Amer. Jour. Science, vol. 35, 1938, p. 401; Bull. Geol. Soc. America, vol. 50, 1939, p. 387. J The moon itself is approximately triaxial and solid (crystallized). 410 Strength of the Earth-Shells activity is probably in large part responsible for the present vitreous state of the asthenosphere, it does not suffice to pre vent a net cooling of our planet. On this assumption we could admit a thickening of the pressure-solid shell at rates that differ in the sial-richer land hemisphere and the sial- poor water hemisphere. And our guessing should carry us into still a third field of unsolved problems. The development of mountain roots and the associated stoping of the relatively cool rock of the lithosphere must have somewhat chilled the asthenosphere and possibly have caused special thickening of the meso spheric shell under the respective orogenic belts. On a much larger scale similar disturbance of the earth’s internal tem perature would be an expected result, if continents have mi grated to considerable distances in Cenozoic time—a process not yet to be excluded from the working hypotheses of dynamical geology. CONCLUSIONS No worker in earth science enjoys insecure premises. This chapter has plunged the reader to an almost intolerable depth in the fog of uncertainty, as a speculative picture of the earth’s interior has been drawn. For the picturing some solid facts are available, but little progress could be made without some guessing about the complex mystery. We have seen that a theory of isostasy, based on the postu late of perfect weakness of the asthenosphere, is practically untenable unless the figure of the earth departs from the shape of a rotation-spheroid. There is more hope for that theory of “ideal” isostasy if Heiskanen’s 1938 triaxial for mula for the geoidal figure is true in principle. A correla tion of the triaxiality with the existence of a strengthless asthenosphere has been attempted. Several assumptions are made: first, that the weakness of the asthenosphere is Strength of the Earth-Shells 411 due to its vitreous state and accompanying high tempera ture; second, that the mesospheric shell is strong because it is crystallized by pressure; third, that the intrinsic density of the asthenosphere is smaller than the intrinsic density of the mesospheric material immediately beneath; fourth, that the surface of the mesospheric shell departs from the form of a rotation-spheroid. That surface has not the form of a simple oblate spheroid, but is humped in at least one of the earth-sectors bearing the two major belts of positive anom aly of gravity, and hollowed in the sectors bearing the two major negative belts.* Under these conditions much of the stress indicated by geoidal departures from the figure of a perfect rotation-spheroid must be borne by the mesospheric shell. To that extent, the great loads implied by the four major belts of anomaly would be no tax whatever on the strength of the lithosphere. However, the geoid, while apparently well generalized or averaged as a triaxial spheroid, is likely to depart from this exact figure by broad, irregularly spaced humps and hollows, and these secondary curvatures of the geoid may reflect cor responding secondary curvatures in the surface of the meso spheric shell. In such cases also the loads indicated by fields of one-sign anomaly would be largely borne by the mesospheric shell—by so much decreasing load-stresses in the lithosphere. Orogenic chilling and differential radioactivity have been listed among the conceivable causes for the triaxiality of the mesospheric shell; each process changes temperatures at depth, so as to raise the surface of the mesospheric shell in some sectors of the globe and depress it in others. But the waviness of that surface (its approximation to a triaxial fig- * A bulge of the mesospheric shell in only one hemisphere raises the geoid above the surface of the rotation-spheroid in that hemisphere and also in the opposite hemisphere. See R. S. Woodward, Bull. 48, U.S. Geol. Survey, 1888, p. 82. 412 Strength of the Earth-Shells ure), with corresponding distribution of mass, has suggested an additional cause—one speculatively founded on the cos mogonic relation of earth and moon. The mesospheric inequality would compel a matching de parture of the geoid from the shape of a rotation-spheroid. The gravitational attraction of each mesospheric hump would pile the material of the weak asthenosphere over that hump, having removed this material from the adjacent meso spheric hollows. Sea level would be similarly affected. All three layers—asthenosphere, lithosphere, and ocean—would be brought into approximate conformity with the hump-and- hollow surface of the mesospheric shell. If the mesospheric shell is six per cent denser than the overlying asthenosphere, the equatorial section of the lower shell would depart from circularity by more than five kilo meters and probably less than fifteen kilometers. The cor responding maximum stress-difference in the mesospheric shell would presumably approach the strength of granite at the surface of the earth. A close estimate of the implied minimum strength must be left to the skilled mathematician. A vitreous state for the asthenosphere implies appropriate temperatures in depth. If thermal equilibrium rules, and if the thickness of the asthenosphere were known, we could compute, at least roughly, the temperatures at top and bot tom of the vitreous layer. For at each of these levels the material is at the temperature of melting; permanent under cooling of the glass would be highly improbable. The effect of pressure on the temperature of melting is given by the Clausius-Clapeyronf - 0-024 Xf equation: where dT/dp represents the rate of rise of melting-tempera ture with an increase of pressure by one atmosphere; T rep resents the absolute temperature of melting at one atmos- Strength oe the Earth-Shells 413 phere; and (v2 — iq) represents the difference of specific volumes for the crystalline and liquid phases. Although L and (v2 — zq), and therefore dT/dx, slowly change with depth, we shall not be far wrong in taking a constant value for dT/dx, namely, 3° per kilometer. Fur ther, let us assume the respective temperatures of complete melting for oceanite and peridotite at one atmosphere of pressure to be 1,225° and 1,350°. Allowing for retained volatile matter at the higher pressure, we obtain tempera tures at depth which are not likely to be too low. The result of the simple calculation are given in the following table.
Loci (continental sector) Hypothetical Temperature depth (km) computed
Surface...... 0 + 10° c . Top of vitreous, oceanitic sub-layer, if at...... 60 1,405 Top of vitreous, peridotitic sub-layer, if at...... 80 1,590 Top of vitreous, peridotitic sub-layer, if at...... 100 1,650 Bottom of vitreous, peridotitic sub-layer, and top of mesospheric shell, if at...... 200 1,950 Bottom of vitreous, peridotitic sub-layer and top of mesospheric shell, if at the Jeffreys discontinuity. . . 480 2,790
The results of the computation are crude and troubled by one’s ignorance of the correct values for L and (v2 — iq), especially for the greater depths. Of course, still more seri ous uncertainty must persist until, by seismological or other evidence, the actual thickness and chemical composition of the vitreous layer shall have been demonstrated. Never theless, it is clear that, if the asthenosphere is vitreous and comparatively thin, it must have definite temperatures at its top and bottom. Will future study of this shell lead to a useful extension of range for the “geological thermometer”? If the mesospheric shell extends down to the earth’s iron core, is crystalline throughout, and is chiefly composed of material similar to the stony meteorites, the temperature at 2,900 kilometers below sea level is likely to be much less than 414 Strength of the Earth-Shells 10,000°. On the one hand, the quantity (v2 — iq) affecting the melting-temperature at —2,900 kilometers must be only a fraction of its value at low pressure. And we have already noted the possibility, if not probability, that convection in the young earth produced at the top of the core a tempera ture well below that giving initial liquidity to the stony- meteorite material at the deep level. If the mesospheric shell now averages 500° or more below the mean temperature of melting, the shell would have the considerable strength needed to explain the triaxiality of the planetary figure. A maximum temperature of 4,000° at —2,900 kilometers is conceivable. It would imply, within the shell, an average thermal gradient of only about 1 ° per kilometer of depth. The suggested earth-model demands lithospheric strength in continental areas, perhaps twice that of granite in the testing-machine, and a still greater strength under the deep oceans. It will be recalled that Barrell deduced roughly similar magnitudes, as recorded in his remarkable publica tion of the year 1915. A true crust of the earth is evidently capable of transmit ting horizontal pressure to indefinite distance, if it rests on a thoroughly weak layer; there is no permanent resistance to the horizontal shearing involved in the making of mountain chains. The assumption that the upper part of the asthenosphere was, in former times, basaltic and eruptible leads to a reason able theory of the voluminous plateau-basalts and of igneous action in general. The great bodies of peridotite thrust into the mountain-roots may have originated directly in the vitreous, peridotitic part of the asthenosphere, whether or not this was, at any given level, surmounted by a thin sub layer of vitreous basalt. If the density of the upper part of the asthenosphere is no greater than 2.8 to 3.0, the approximate maxima for vitreous basalt or oceanite and peridotite, the problem of geosyn Strength of the Earth-Shells 415 clinal down-warping becomes much less serious than it is if the asthenosphere is assumed to be crystallized peridotite with density of 3.3. Further, we have seen that the facts of geology, geodesy, and seismology support the mountain-root hypothesis of Airy, Fisher, Heim, and others. And modern geophysical discoveries also in principle support Pratt’s idea of attenua tion. Both hypotheses go far to explain the “vide” detected with plumb-bob and gravity pendulum, under Andes, Pyr enees, and Himalayas. The postulate of a thick, strong, mesospheric shell invites geological speculation. Is it possible that secular and paroxysmal changes in the shape of this shell have been re sponsible for such an utterly mysterious process as the de velopment of orogenic pressure, and even for the failure of the sial over most of the Pacific region? A final, general conclusion: an acceptable solution for the supreme problem of the earth’s interior must be founded on discoveries of physical geologist, petrologist, and seismolo gist, as well as on the observations of experts on terrestrial gravity. Fortunately, there is growing appreciation of the value of co-operation among all these groups of specialists.
R efer en c e s 1. See H. S. Washington, “Internal Constitution of the Earth” (edited by B. Gutenberg, Nat. Research Council, Washing ton), New York, 1939, p. 92. 2. G. H. Darwin, Scientific Papers, Cambridge, England, vol. 2, 1908, pp. 459 ff.; Phil. Trans. Roy. Soc. London, vol. 173, 1882, p. 187. 3. J. Barrell, Jour. Geology, vol. 23, 1915, p. 734. 4. See J. Barrell, Jour. Geology, vol. 23, 1915, p. 44; Amer. Jour. Science (posthumous paper), vol. 48, 1919, pp. 281 and 304. 5. H. Jeffreys, Mon. Not. Roy. Astr. Soc., Geophys. Supp., vol. 3, 1932, p. 41. 416 Strength of the Earth-Shells 6. J. Barrell, Jour. Geology, vol. 23, 1915, p. 44. H. Jeffreys, “The Earth,” second edition, 1929, p. 230; Ergebnisse der kosmischen Physik, Leipzig, vol. 4, 1939, p. 95. 7. J. Barrell, Jour. Geology, vol. 22, 1914, p. 235. 8. R. A. Daly, Jour. Washington Acad. Sciences, vol. 25, 1935, p. 389. 9. F. A. Vening Meinesz, “Gravity Expeditions at Sea,” Delft, 1934, vol. 2, p. 135. 10. J. Barrell, Amer. Jour. Science, vol. 13, 1927, p. 303. 11. See J. Barrell, Jour. Geology, vol. 23, 1915, p. 37, quoting from F. R. Helmert, Encyc. math. Wissenschaften, vol. 6, part IB, Heft 2, 1910, p. 133. 12. J. Barrell, Jour. Geology, vol. 23, 1915, p. 33. 13. See E. A. Glennie, Geodetic Report, Survey of India, vol. 5, 1930, p. 56; also chart in vol. 8, 1933. 14. F. D. Adams and L. V. King, Jour. Geology, vol. 20, 1912, p. 97. 15. D. T. Griggs, Jour. Geology, vol. 44, 1936, p. 557; ibid., vol. 47, 1939, pp. 227 and 234. 16. E. Niskanen, Annales Acad. Sci. Fennicae, ser. A., vol. 53, No. 10, 1939, pp. 16 and 26. 17. S. Timoshenko, “Theory of Elasticity,” New York, 1934, p. 350; Dean H. M. Westergaard of the Harvard Engineer ing School kindly drew the writer’s attention to the diagram. 18. See L. M. Hoskins in “Geology,” by T. C. Chamberlin and R. D. Salisbury, New York, 1906, vol. 1, p. 581. 19. The calculations were made from formulas at p. 461, “Me chanical Engineers’ Handbook,” edited by L. S. Marks, New York, third ed., 1930. 20. W. Heiskanen, Report on Isostasy, Internat. Union of Geodesy and Geophysics, Washington meeting, 1939 (mimeographed edition); compare also the Survey of India Report on Geodetic Work for the period 1933-1939, pre pared for the same meeting (section on intensity of gravity at Dehra Dun). 21. See R. A. Daly, “Igneous Rocks and the Depths of the Earth,” New York, 1933, pp. 263 ff. 22. J. F. Hayford, Supplementary Investigation in 1909 of the Figure of the Earth and Isostasy, U. S. Coast and Geodetic Survey, 1910, p. 58. Strength of the Earth-Shells 417 23. J. Barrell, posthumous paper in the Amer. Jour. Science, vol. 48, 1919, p. 331. 24. H. Jeffreys, Ergebnisse der kosmischen Physik, Leipzig, vol. 4, 1939, p. 94. 25. P. W. Bridgman, Jour. Geology, vol. 44, 1936, p. 666; Proc. Amer. Acad. Arts and Sciences, vol. 71, 1937, p. 412. 26. H. Jeffreys, Ergebnisse der kosmischen Physik, Leipzig, vol. 4,1939, p. 94. 27. R. A. Daly, “Igneous Rocks and the Depths of the Earth,” New York, 1933, pp. 267 ff. and 311 ff. (with further refer ences); “Architecture of the Earth,” New York, 1938, chapters 3 and 5. 28. P. W. Bridgman, personal communication. See also his papers, especially that in the Proceedings of the American Academy of Arts and Sciences, vol. 72, 1937, p. 45. After the present book had reached the stage of page proof, J. Lynch (Science, vol. 92, 1940, p. 10) suggested the possibility that a deep-focus earthquake may be caused in the following way: “The quake or fracture actually occurs comparatively near the surface but . . . a real image of it is formed some hundreds of miles down, and it is from this focal point that the seismologist’s waves start.” The waves with energy sufficient for recording by the seismograph may thus come from a “real image” of the hypocenter, the real image being developed in the asthenosphere because this layer, having little or no strength, is elastico-viscous and highly rigid. Lynch conceives the parabolic mirror, re sponsible for the real image, as formed by mountain roots of the Airy type. Apparently his idea may be extended to cover the hypothetical case where the fracture and original shock were located in the mesospheric shell, assumed to be crystallized by pressure and therefore of considerable strength. 29. B. Willis, Ann. Report of the Smithsonian Institution for 1910 (1911), p. 391; J. Barrell, Jour. Geology, vol. 22, 1914, p. 34. INDEX
A Anomalies of gravity (Cont.): crust-warp type, 240, 245 Adams, F. D., 384, 416 extended-Bouguer type, 118 Adams, L. H., 19 free-air type, 149 Adhemar, J., 51 Hayford type, 128, 149, 164, 258 Adriatic Sea, gravity on, 197, 200 Heiskanen type, 189 Africa, East, gravity in, 127, 218, 223, indirect-isostatic type, 128 250, 344 in glaciated tracts, 323, 330 Airy, G. B., 37, 42, 43, 64, 82, 224, 415 in relation to the geoid, 194, 382 Airy type of isostatic compensation, 45, in relation to the height of station, 47, 48, 49, 55, 56, 59, 97, 121, 162, 180, 190, 206, 208, 248, 171, 188, 203, 343 342 compared with (Pratt-)Hayford type, in relation to the spheroid of refer 187, 262, 306 ence, 149, 344 Aland Islands, 326 in terms of masses, 154 Alaska, gravity in, 161 modified-Bouguer type, 119 Algonquin beach, 327, 328 on mountains of circumdenudation, Algonquin hinge-line, 327, 390 172 Alps: over ocean, 259, 290 average height, 204 regional type. 124, 152, 166, 171, 186, degree of isostasy, 216 197, 206,' 240, 257, 259, 273, 290, gravity on, 197, 200, 201, 283 295, 299 root of, 198, 201, 202, 204, 283, 285 Anomalies of mass, 111, 114, 200, 232, Amplitudes of uncompensated loads, 252 52, 102, 104, 193, 337, 343, 354, Ansel, E. A., 198 361, 380 Antarctica, recent uplift of, 319, 347 Ancylus Lake stage of Fcnnoscandian Anti-roots, 60, 61, 343, 348 history, 312 Apennines, gravity in, 197, 200 Andes, isostatic compensation of, 36, 38, Appalachian Mountains, isostasy in, 342, 415 50 Angle of depression, 89, 90, 141, 148 Arabian Sea, gravity on, 238, 369 Ankaramite, 19 Arctic Ocean, degree of isostasy of, 253 Anomalies of gravity, 54, 114, 129, 149, Areas of anomaly: 348, 362 degree of permanency, 338, 352, 385 Airy type, 188 dimensions, 52, 102, 104, 105, 181, along the Atlantic slope of North 193, 233, 238, 337, 343, 354, 361, America, 189, 191 380 along the Pacific slope of North Aristotle, 26 America, 189, 191, 193 Arkansas, peridotite in, 20 Bouguer type, 120, 149 Ascension Island, gravity on, 302 419 420 Index Asia: Barrell, J. {Coni.): gravity in, 347 crustal bulge peripheral to glaciated in relation to East Indian “strip,” tract, 320 280, 284 defect of mass under ocean Deeps, 380 Asthenosphere, 3, 5, 13, 14, 15, 16, 309 distribution of strength in the earth, Asthenospheric shell: 4, 13 composition, 16 explanation of height of the western density, 375 Cordillera, 395 fracture, sudden, 404 explanation of mediterranean basins, in relation to deep-focus earthquakes, 376 400 gravitational effects of local abnor in relation to diastrophism. 15, 398 malities of rock density, 351 in relation to ideal isostasy, 13 relation of gravity anomaly to height in relation to peneplains, 407 of station, 170 in relation to petrogenesis, 15, 398, relation of warped peneplains to 400 theory of isostasy, 407 strength, 13, 193, 309, 320, 334, 350, strength of asthenosphere, 353, 358, 355, 375, 388, 390 360 temperature, 413 strength of continental crust, 306, theoretically deduced strength, 250 353,357,383 thickness, 15, 320 strength of lithosphere, 358 viscosity, 13, 59 strength of sub-Pacific crust, 379, 383 vitreous state, 19, 398 stress-differences due to uncompen Atlantic Ocean, gravity on, 255, 261, sated loads, 356,357 350,371 test of hypothesis of local compen Attenuation, a cause of isostatic com sation, 167 pensation, 37, 41, 47, 282, 407, types of isostatic compensation, 62 415 uncompensated load around Pikes Attraction: Peak, 171 of a mass, 66, 82, 107, 116, 143, 165, uncompensated loads in the United 167 States, 102, 362 of an extended plate, 116 Bartlett Deep, 293, 294 Australia, in relation to East Indian Basaltic layer (substratum), 18, 19, 414 “strip,” 284 Basement Complex, 17 Austria, gravity in, 161 Base station, 113, 392 Average-level anomaly of gravity, 124, Basevi, J. P., 50 185 “Basic” rock, 18 Azimuth, 67 Batholith, in relation to lithospheric Azores Islands, gravity around, 301 strength, 394 Beaches, raised, 212 B Bellamy, C. V., 212 Bemmelen, R. W. van, 270, 389 Babbage, C., 38, 48, 63 Benfield, A. E., 108, 129 Baltic Geodetic Commission, 4, 130 Berchtesgaden region, excess mass in, Baltic Sea, 311 202 Bancroft, D., 5 Bergsten, F., 314, 335 Banda Sea, gravity on, 264, 273, 373 Berlage, P., 389 Banggai Island, 270 Bermuda Island, 161, 302 Barrell, J., 64, 67, 165, 167, 194, 308, Berroth spheroid of reference, 32 335, 352, 409, 415, 416, 417 Bessel, F. W., 28, 30 Barrell, J., on: Birch, F.; 5, 19 anomalies in Hawaii, 379 Black Forest, uncompensated load in, anomaly field of United States, 167 201 center of gravity of compensation, 62 Black Sea, gravity on, 201, 255 Index 421 Bohemian massif, gravity in, 201 Brownson Deep, 288, 377 Bombay, upwarp of crust under, 246 Buckling hypothesis in relation to Bomford, G., 231, 251, 368 orogeny, 275, 278, 282 Born, A., 199, 201, 217, 219, 251, 283 Bulge, topographic, due to imperfect Borrass, E., 196, 216 isostatic adjustment, 51, 59, 277, Boscovich, R. J., 36, 37, 38, 48, 63, 82, 290, 319 85 Bullard, E. C., 127, 136, 183, 219, 221, Bouguer, P., 36, 38, 41, 50, 82 222, 250, 251, 296, 348, 349, 372 Bouguer anomalies of gravity, 149, 162, Bullen, K. E., 21, 22. 24, 35 196 Burrard, S. G., 140, 228, 245, 352 at ocean Deeps, 378 Byerly, P., 192, 195 at sea, 119, 120, 258, 343 extended, 118 C modified, 119 test of isostasy, 58, 116, 118, 120, 158, California, anomalous field of, 163, 189, 272, 306, 342 191, 193, 245, 351 Bouguer reduction of gravity, 114, 116, Calumet lake-gage, 326-327 124 Canada: Bowie, W., 4,31,131,159, 236, 305,308, eastern, Pleistocene (post-Pliocene) 340 upwarping in, 319 reports by, 159, 174 gravity in, 131, 160, 190, 192 Bowie, W., on: Canadian Dominion Observatory, 4 change of sign for effect of topography Cape Comorin, 42, 226, 229 and compensation, 147 Carelia, gravity anomalies in, 336 densities in the lithosphere, 165, 177, Caribbean Sea, gravity on, 285, 373 181,351 Carinthian Lakes region, defect of mass departures from isostasy, 175, 178 in, 202 effect of changing assumed depth of Carpathian Mountains, gravity in, 200 compensation, 173, 178 Cassinis, C., 4, 253, 264, 307, 348 effect of elevation on the intensity of Catalogue of world gravity data, 129, gravity, 168, 180 197, 213, 224, 238, 249, 265, 348, formulas for spheroid of reference, 32, 372 160 Caucasus, gravity in, 205, 216, 342, 349 isopiestic level, 181 Celebes Island, 20, 270 isostasy in the United States, 34, 163, Celebes Sea, 266, 273, 373 174, 182 Center of gravity of compensation, 62, isostasy in the West Indies, 289 198, 348 isostatic compensation, 48 Centrifugal force, 109 local versus regional compensation, Centrosphere, 13, 355, 409 168 Ceram Island, 270 relation of geoid to standard spheroid, Ceylon, gravity anomalies in, 237 79 Chablais Alps, 200 tests of isostasy, 164, 182 Chamberlin, R. T., 351, 352 triaxial figure for the earth, 177 Chamberlin, T. C., 97, 99 Bowie reduction (see Indirect reduction Chandler motion of the poles, 31 of gravity) Change of sign of resultant effect of Bowie spheroids of reference, 32, 160 topography and compensation, Bridgman, P. W., 5, 19, 402, 403, 404, 146 406, 417 Chilling, orogenic, 398, 406, 411 Brillouin reduction of gravity, 128 Christmas Island, 280 Brown, E. W., 30 Clark, II., 5 Brown, T. T., 257 Clark, J. S., 113 Browne, B. C., 257, 307 Clarke, A. R., 28, 30, 71, 82 Browne term, 258, 260 Clarke ellipsoid, 67, 69, 78, 92 422 Index Clarke spheroid of 1880, 187 Correction in reduction of gravity, Clausius-Clapeyron equation, 412 (Cont.): Clearing-house for systematic record of for effect of topography, 140 gravity data, 129 for elevation, 139 Cleveland lake-gage, 328 Costanzi, G., 197, 216 “Coast effect,” 54, 244, 298, 371 Councilman, H. J., 239 Coasts, gravity profiles off, 294, 295, Crests, gravity, 226, 241 298 Crimea, gravity in, 215 Collins, E. B, 257 Criteria for isostatic hypotheses, 92, Compartments, topographic, 73, 136, 209, 343 140 Croll, J., 51 Compensation, isostatic, 5, 12, 36, 48, Crosthwait, H. L., 239 84, 85, 340 Crust, earth’s (see also Lithosphere), 38, center of gravity, 178, 193 97, 121, 340, 395, 399 complete, 94. 100, 135 definition, 5, 15, 47, 229 decrease, with depth, 193 flexural strength, 328 degree, 99, 101, 104, 157 horizontal displacement, 3, 399 depth, 12, 53, 55, 58, 82, 84, 93, 96, orogenic shortening, 278, 401 136, 154, 173, 207, 350 recoil, 318 effect on computed gravity, 146, 348 thin, floating stress in, 359 in layer at depth, 49 Crust-warp anomalies, 240, 245 layer (zone), 12, 15, 178 Crust-warping, 126, 211, 221, 229, 230, local, 58, 84, 152, 168, 193 241, 246, 259, 277, 285, 300, 339, mountain, 235 399 of composite nature, 62, 364 Crystallinity (?) of third layer, 18 regional, 47, 52, 59, 60, 104, 125, 152, Crystallization by pressure, 411 168, 171, 172, 221, 236, 240, 250, Cuddapah sediments, thickness of, 246 319 Curvature of earth, affecting gravity at test, 99, 102, 111, 184 station, 117, 148 theories, 56, 58, 62, 121 Cyprus, gravity in, 211, 216 to uniform depth (Hayford), 58, 87, 137 D uniformly distributed in depth (Hay- ford), 58, 86, 94, 96, 104 Daly, R. A., 308. 318, 335. 336, 415, Compressibility, 23 416, 417 Compression of lithosphere: Damaridga station, India, 39, 42 horizontal, 197, 250, 276, 391 Dane, E. B., 5 source of lithospheric strength, 391 Darling, F. W„ 127 Conrad, V., 217 Darwin, G. H.. 97. 353, 388, 415 Continental shelf, 296 Davis, W. M., 333 Continental slope, 54 Dead Sea, 115 Continents: Deccan trap, 245 isostatic support, 47, 53, 83 Deecke, W., 197, 216 origin, 3 Deep-focus earthquakes, 355, 400 Contraction theory of mountain chains, Deeps, ocean, gravity over. 255, 278, 284, 402 290, 347, 376. 378 Convection, thermal, 267, 397 Deficiency of mass, 40, 133, 248 Convection currents, in relation to grav Deflection of the plumb line, 24, 26, 33, ity anomalies. 267. 278, 284, 374 50, 65, 68, 156, 226, 252 Cook, G. S., 113 affected by isostatic compensation, Core, earth’s, 1, 13, 21, 24, 397, 404, 413 45, 87, 91 Correction in reduction of gravity, 117. computed versus observed, 45, 77, 92 139 formulas for computing, 89 for effect of compensation, 140 in the meridian, 68, 105 Index 423 Deflection of the plumb line, (Coni.): Earth, (Coni.): in the prime-vertical. 69, 105 338 (see also Ellipsoid, Geoid, residuals, 27, 33, 42, 92, 95, 103 Spheroid) topographic, 70, 77, 91 gravity in interior, 86 Deformation of rocks, 7 internal densities, 22 Deglaciation and uprise of lithosphere, mantle, 1, 21, 354, 397, 404 337 mass, 17 Dehra Dun, India: mathematical figure, 25, 28, 30, 31 absolute gravity at, 392 mean density, 17, 21, 57 base station at, 392 moment of inertia, 21, 24, 31, 57 Delambre ellipsoid of reference, 30 original organization, 396 Deltas, gravity on and near, 303 physical figure, 26, 52 Denmark, mean gravity anomaly in, plasticity, 37, 51 372 self-compression, 23 Density, abnormalities of: size, 26, 33 at and near earth’s surface, 33, 41, Earthquakes, 276, 291, 351, 385 53, 66, 82, 94, 122, 165, 351, 370 East Africa, gravity in, 127, 218, 219, in relation to depth, 12, 57, 82, 359 223, 250, 344 intrinsic, 23, 375, 411 East Indian “strip” of negative anom mean, at earth’s surface, 21, 72, 134 aly, 268, 269, 271, 272, 278, 285, mean for the ocean, 73 288 mean for the whole earth, 21, 72 East Indies: of the asthenosphere, 23 gravity in, 269 De Sitter, W., 30 orogeny in, 267, 279 Diastrophism in relation to the earth- sea basins, 266, 374 shells, 3, 15, 398 Elastic after-working, 317, 384 “Dichteschwelle,” 200 Elastic limit, 8, 9, 384 Differentiation, gravitative, 397 Elastic moduli 18 Dikes of peridotite, 20 Elasticoviscosity, 5, 9, 10, 404 Dimensions of anomalous areas, 181 Elastic reaction of lithosphere to load, (see also Amplitudes and Spans) 328 Discontinuities in the earth, 1, 13, 16, Ellipsoid: 21, 22, 61, 277 a figure of the earth, 24, 25 Dow, R. B., 5 of reference, 28, 67, 82 Downwarping of lithosphere, 243, 284 rotational (of revolution), 25, 109 Drau region, excess mass in, 202 triaxial, 25, 346, 404 Dunite, 18 Ellipsoids of reference, 28, 102 Dunitic layer, 18, 242 Ellipticity of the earth, 25, 26, 30, 110 Durovitreous state, 10 Eotvos balance, 57 Dutton, C. E., 11, 51, 53, 236, 340 Epeirogenic warping, 317 Dyne, 106 Equator, shape of, 25 Equatorial ellipse, 25, 32 E Equipotential surface, 25, 78, 83, 114 341 Earth: Eratosthenes, 26 core of, 1, 13, 21, 24, 397, 404, 413 Erola, V., 247, 251 determining the figure of, 36, 65, 82, Erosion, 14, 37, 157, 243, 252 92, 102 Errors in computation: discontinuities, 1, 13, 16, 21, 22 of deflection residuals, 93 distribution of mass, 17 of gravity anomalies, 348 distribution of strength, 2, 58, 102 Europe in general, gravity in, 131, 160, elastic distortion, 24 161, 199, 205, 207, 213, 215 ellipticity, 25, 26, 30, 110 Eustatic shifts of sea level, 51, 212, 321, geoidal figure, 16, 24, 28, 65, 67, 106, 332 424 Index Everest, G., 30, 38, 224, 238 Finland (Cont.): Ewing, J. A., 6, 296 gravity in, 210, 323, 325, 344, 386 Excess of mass, 40, 134 relief, 323 Expansion of lithosphere, vertical, 36, upwarping, 314, 315, 387 41, 62 Fisher, E. G., 112 Experiments on strength of rock, 8, 384 Fisher, O., 99, 229, 415 “Extended” Bouguer correction, 118 Flexural strength of the lithosphere, 393 Flow in isostatic adjustment, 12, 37, 38, F 50, 51, 53, 284, 311 Foreland, mountain, gravity in, 201 Factors: Fracture-warps of the lithosphere, 250, for computing deflections of plumb 277, 377 line, 88, 91 “Fram” expedition, measurements of for computing gravity anomalies, 122, gravity by, 252 20S France, mean Airy anomaly in, 372 Faroe Islands, 319 Free-air anomalies of gravity, 149, 196 Fault-troughs, gravity in, 211, 218 largest known, 212 Fennoscandia, 213, 355 (see also D en Free-air reduction of gravity, 114, 124 mark, Finland, Norway, Swe Freeman, J. R., 326, 336 den) Fugitive elasticity, 10 center of icecap of, 313, 323, 329 Furtwangler, P., 130 compared geophysically with India, 365, 390 G crust-warping, 316 current warping of surface, 215, 314, “Gabbroic” layer, 18, 61 335 Gal defined, 31, 106 degree of isostasy in, 322 Galileo, 106 eustatic changes of sea level, 321 Ganges alluvium, 39, 225, 228, 244, 351 future upwarping, 387, 393 Ganges gravity trough, 227, 230, 234, gravity in, 322, 386 364, 392 hinge-lines (hinge-zones), 322 Gas, rise of, in asthenosphere, 405 icecap, 310, 313, 323 Geliindereduktion, 118 isobases, 311, 313 Geoid, 24, 25, 78 marine limit, 313, 319 compensated, 231, 234, 382 Pleistocene (i.e., post-Pliocene) warp construction, 77 ing, 310, 312, 322, 329 Cordilleran segment, 105 precise leveling, 315 in central Europe, 324 “quasi-orogenic” displacements, 322 in Cyprus, 212 stages of Pleistocene history, 311, 313 in India, 176, 225, 230, 231, 234 strandflat, 330, 331 in relation to areas of gravity anom tide-gage studies, 313 aly, 157, 382 Ferghana Basin, gravity in, 247 in Switzerland, 127, 205 Fernando de Noronha Island, 302 in United States, 77, 80, 81, 235 Figure of the earth (see also Earth): natural, or actual, 25, 228, 229, 234, biaxial, 25, 30, 31 241 definition, 24 reduction of gravity to, 111 geoidal, 26 relation to topography, 80 mathematical, 26, 177, 196 relation to vertical, 83 physical, 26, 78, 84 wavy shape, 25, 28, 32, 77, 79, 81, 83, triaxial, 25, 31, 33, 177, 306, 320, 341, 105, 126, 175, 241, 411 373 Geoidal height related to gravity anom Finland (see also Fennoscandia), 215 alies, 194, 241 current changes of level, 315 Geological data in problems of isostasy, Geodetic Institute, 4, 187 57, 63, 310, 350 Index 425 Geosynclines, 50, 245, 246, 280, 415 Gulf of Bothnia, 323 Germany, gravity in, 161, 200 Gulf of Mexico, gravity on, 264, 266, Gilbert, G. K., 53. 64, 187, 194, 326, 306, 373, 376 336, 394, 409 Gutenberg, B., 1, 4, 18, 21, 35, 128, 171, Glaciated tracts: 188, 198, 217, 326, 336, 403, 415 degree of isostasy in, 194, 210, 351, 385 H list of, 318 Haalck, H.. 112, 130 upwarping in, 210 Hall, J., 50, 64 Glennie, E. A., 4, 126, 211, 229, 240, Halmaheira Island, 270 242, 250, 285, 339, 352, 382, 399, Hansen, S., 252, 253 416 Harmonics, spherical, 25, 29 Goldthwait, J. W., 327 Harz Mountains, degree of isostasy in, Gosschkoff, P. M., 224 207, 214, 285, 349 Grabens, gravity in, 211, 218 Haskell, N. A., 389 Granitic layer, 18, 20, 24, 198, 242 Hawaii, 379 Gravimeter, 50, 60, 112. 196, 253 Hawaiian Islands, 20, 299, 378, 380, 383 Gravitation, law of, 106 Hayford, J. F.: Gravitational constant, 106 assumptions for testing isostasy, 84, Gravitational survey of the earth, need 86, 92, 97, 416 of extending, 345 first test of isostasy with plumb line, Gravity: 67, 70 absolute, 112, 113 on assumed constancy of gravity in anomalies, 33, 54 computations, 86, 109 in relation to geoidal warps, 194 on comparison of types of isostatic in spite of isostasy, 166 compensation, 92 at equator, 109 on construction of geoid in the United at sea, 112, 116, 252, 256 States, 78 computed, 137, 148 on deflections of the plumb line in field of, 57, 108 the United States, 28, 103 force of, 3, 16, 24, 86 on depth of isostatic compensation, formulas, 29, 31 55 in relation to height of station (see on errors of mensuration and compu Anomalies of gravity) tation, 72, 93 measurement, 111 on reduction factors, 90 profiles off shores, 54, 244, 294, 295, on zones (rings) and compartments, 298, 371 70, 119 reduction of values, 114 recognition of isostasy by, 33, 81, 104 theoretical, 55, 114, 139, 148 reports by, 67, 102, 131 troughs, 226, 229, 234 second test of isostasy with plumb variation of: line, 102 in depth, 86, 108, 135 Hayford-Bowie: in the meridian, 86, 109, 135 assumptions in computing gravity, Great Britain: 121, 132, 136, 152 icecap, 310 general conclusions regarding isos mean gravity anomaly, 372 tasy, 156, 342 Great Lakes, 326, 327, 328 hypothesis of isostasy, 132 Greenland: on comparison of Hayford and other basining under icecap, 319 types of anomaly, 150 recent uplift, 319, 347 on corrections for topography and Greenwich-Capctown arc, 30 compensation, 140 Gregory, J. W., 223 on depth of isostatic compensation, Griggs, D. T., 5, 7, 8, 9, 34, 384, 416 154 Guillaume, E., 253, 307 on errors in data, 152 426 Index Hayford-Bowie {Coni.): “Heiskanen anomalies,” as synonyiri on interpretation of gravity anom for “Airy anomalies,” 220, 258 alies, 155 Heiskanen triaxial formulas: on local versus regional compensa of 1924, 31, 208, 221 tion, 152 of 1926, 30 on rings (zones) and compartments, of 1928, 31, 221 140 of 1938, 30, 221, 250, 263, 285, 320, on size of uncompensated loads on 323,345,369 lithosphere, 156 Heiskanen type of isostatic compensa reduction tables, 141 tion, 49, 122, 343 reports on gravimetric tests of isos- Helgeland, 334 tasy, 131 Ilelmcrt, F. R., 54, 64, 82, 110, 128, spheroid of reference, 34 196, 202, 293, 307, 379 Hayford ellipsoid of reference, 28, 29, ellipsoid of reference, 30, 31 30, 82, 102 spheroid of reference of 1884, 32, 253 Hayford gravity anomaly, 148, 164 spheroid of reference of 1901, 32, 138, Hayford hypothesis of isostasy, 84 150, 173, 188, 196, 239 Hayford type of compensation, 48, 49, triaxial spheroid of 1915, 32, 177 56, 86, 231, 236, 339 Helsinki base station, 210, 211 Hecker, 0., 112, 219, 252, 255, 291, 307, Herschel, J., 37, 48, 50 377 Hess, H. H., 257, 285, 288, 308 Height of station in relation to gravity Heyl, P., 113 anomaly (see Anomalies of grav Hidden Cause, 42, 225, 230 ity) Hidden Range, 227, 228, 230, 237, 241, Heim, Albrecht, 198, 200, 216, 415 245, 352, 367, 382 Heiskanen, W., 4, 64, 118, 128, 130, 140, High Asia (Himalaya-Tibet), 39, 42, 171, 194, 202, 216, 242, 251, 255, 224, 226, 342 285, 303, 308, 334, 347, 352, 393, Himalayas, 40, 50, 176, 224, 226. 235, 416 237, 280, 342, 415 assumptions of densities in depth, Hinge-lines (hinge-zones), 388 122, 188 Hinks, A. R., 339, 352 compiler of world Catalogue, 129, 197 Hirvonen, R. A., 31, 210, 323, 336, 386, director of Isostatic Institute, 129 393 hypothesis of isostatic compensation, Hokkaido Island, gravity in, 249 49, 123, 188 Holweck, F., 112, 130 modification of Airy isostatic hy Hondo Island, gravity in, 249 pothesis by, 122 Honolulu, 302, 379, 383 on tests of isostatic hypothesis: Horizontality of Algonquin and Whit in Alps, 204 tlesey beaches, 327 in Caucasus, 205 Horn, E., 282, 308 in central Europe, 205 Hoskins, L. M., 416 in Japan, 248 Hoskinson, A. J., 285 in Lofoten Islands, 210 Hudson Bay, center of icecap, 329, 347 in Norway, 161, 208, 334 Hughson, W. G., 191, 195, 329, 369 in Spitsbergen, 207 Hunter, J. de G., 30, 231, 251, 339, 368 in United States, 187, 190 Hydrodynamical equilibrium, 340 in West Indies, 290 on validity of principle of isostasy, 63, I 338, 340 reduces observed gravity to sea level Icecaps: (geoid), 121 and isostasy, 51, 310, 318, 389 reference ellipsoids computed by, 30 centers of, 323, 326, 329, 386 reference spheroids computed by, 32, Iceland, isostatic recoil of, 311 325 Ide, J. M., 5 Index 427 Igneous action, 3, 18, 219, 399, 400 Isostasy (Cont.): India: actual, 15, 21, 52, 341 Airy on isostasy, 42 an exceptional condition (Jeffreys), anomalies of mass, 232 400 areas of one-sign anomaly, 228, 233, a tendency, 11, 14, 52 237, 239, 240 at sea, 252 compared geophysically with Fen- ideal, 11, 13, 52, 250, 306, 341, 360, noscandia, 365, 390 410 compared geophysically with United principle of, 4, 14, 34, 36, 48, 81, 225, States, 238, 380 235, 309, 339 crust-warping, 230, 240, 245 tests, 54, 65, 92, 102, 105, 116, 118, current warping, 368 125, 158, 188, 234, 255, 316 deflection of plumb line, 40, 42, 226 Isostatic adjustment, 4, 5, 12, 38, 50, 53, degree of isostasy, 224, 241, 342, 347, 84, 311, 334, 386 354 Isostatic anomaly, largest positive, 212 geoid in relation to anomaly field, 233 Isostatic compensation (see Compensa geoids, 176, 225, 228, 230, 231 tion, isostatic) gravitational crest, 228, 242 Isostatic hypotheses, 56, 92, 108 gravitational troughs, 230, 242 Isostatic Institute, 129 gravity, 38, 132, 218, 236 Isostatic reduction of gravity, 114, 120, Hayford anomalies, 232, 237, 239 125 Hidden Range, 226, 354 Italy, gravity in, 161, 213, 214 peneplain, 225 Ivrea zone, 200 precise leveling, 368 preferred reference spheroids for, 239, J 366 Jamieson, T. F., 50, 64, 310, 316 regional compensation, 243 Jamieson hypothesis, objections to, 316, strength of lithosphere under, 238, 319, 330 250, 364, 392 Japan, gravity in, 161, 218, 248, 250 Survey of, 4, 5, 29, 140, 224 Japan Deep, gravity on, 249, 292, 377 tripartite gravity field of peninsula, Java Deep, 274, 293, 377 42, 226, 366, 391 Java Sea, 266 uncompensated loads, 380, 381, 392 Jeffreys, H., 4, 34, 35, 415, 417 upwarping tendency of southern, 392 on deep-focus earthquakes, 400 Indian Ocean, gravity on, 255, 342 on definitions of terms, 7, 9 Indirect reduction of gravity, 126, 128, on discontinuities in earth, 18, 20, 242 183, 259, 348 formula for calculating stress- Indo-Gangetic plain, gravity in, 225, difference in earth’s crust, 359, 226, 368 381 Initial-Littorina stage of Fennoscandian isostasy, 400 history, 312 strength in the earth, 4, 7. 361 Interglacial stages, 332 stresses in non-isostatic earth, 354. Intermediate rock layer, 18, 20, 24, 242 358, 388 International ellipsoid of reference, 30 Jeffreys discontinuity, 20, 21. 22, 404 International Geodetic Commission, 28 Jolly, H. L. P, 372 International spheroid of reference, 33, Jukes-Brown, A J., 212 34, 129 Jung, K., 4, 128, 339, 352 Interpolation, principle of, 75, 145 Jungfrau, gravity at, 204 Intrinsic density, 23, 375, 411 Jura Mountains, Bougucr anomalies of, Isanomalies, 198 200 Isopiestic level, 12, 14, 48, 49, 61, 181 Isostasios, 11, 52 K Isostasy, 5, 11, 52, 309, 338 Kaliana station, India, 38, 39, 42 a condition, 11, 14 Kalianpur station, India, 38, 39, 42 428 Index Karakoram Mountains, 247 Listing, J. B., 25 Kater, H., 112 Lithosphere, 5, 13 (see also Crust) Kei Island, 270 flexibility, 343 Kelvin, Lord, 396 strength, 15, 59, 309, 354, 379, 393, Kentucky, peridotite in, 19 396 Kerguelen Island, 319 stresses, 13 Kimberlite, 20 sub-layers, 18 King, L. V., 384, 416 thickness, 53, 259, 337, 343, 355 Knopf, A., 38, 63 in past eras, 20. 355, 376, 396, 398 Kober, L., 283 thickness, 355, 393 Kohlschutter, E., 218, 221, 251 Lithospheric shell, 13 Kola peninsula, gravity in, 211 Lithuania, gravity in, 213, 214, 390 Kossmat, F., 198, 200, 216 Littorina beach, 313, 315 Krenkel, E., 218, 251 Loads: Kiihnen, F., 130 borne bv the lithosphere, 105, 213. Kiihnen, P. H., 267, 276, 279, 285, 374, 337* 380 376 borne by the mesospheric shell, 411 Kukkamaki, T. J., 315, 335 in continental areas, 306, 381 in oceanic areas, 306, 383 L Lofoten Islands, anomalies in, 210 Longitude: Labrador icecap, 326, 329 astronomic, 68 Lake Albert, 222 geodetic, 67 Lake Bonneville, warping at, 347, 394 term, in reference formula, 31, 323 Lake Constance, gravity anomaly at, Longitudinal wave, 18, 21 202 Longwell, C. R., 38, 64 Lake Erie, 329 Lopoliths. 23, 211 Lake Geneva, 200, 202 Love, A. E. H., 353, 358 Lake Ladoga, gravity anomalies near, Lunar parallax, 30 211 Lake Michigan, 329 M Lake Superior, topographic deflection Mace, C., 212, 217 at, 76 Madeira Island, 302 Lake Tanganyika, gravity profile at, Madras, gravity trough near, 365 222 M agma, 3 Lambert, W. D., 4,30,35,113,127,129, Maire, C., 63 348 Mantle of earth, 1, 21, 354, 397, 404 “Landscape” correction in reduction' of Maps, world, aids in isostatic reduction, gravity, 118 129 Latitude: Marine limit, 319, 334 astronomic, 38, 40 Marks, L. S., 416 geodetic, 38. 67 Mass, anomalies of, 86, 111, 114, 200, geographic, 109 232, 252 variation, 31 Matuyama, M., 4, 249, 253, 293, 308, Law, R. R., 5 377 Leet, L. D., 5 Maui Island, Hawaii, 302 Lehner, M., 171, 194, 197 Mauna Kea, Hawaii, 302, 379 Lejay, P., 112, 130 Mauritius Island, 302 Letti Island, 270 Meades Ranch, United States Standard Level: Datum , 68 current changes (see Fennoscandia, Mediterranean basin of Europe, over- Finland, India) compensation in, 207, 264 eustatic shifts of sea, 51, 212, 321,332 Mediterranean seas, gravity on, 264, Liquevitreous, 10 287, 306, 372, 375 Index 429 Meissner. O., 55 “New-method” reduction of gravity, Mendenhall, T. C., 112 150 Mesosphere, 13, 355 New York State, peridotite in, 20 Mesospheric shell: New Zealand, “ultra-basic” intrusions asymmetry, 405, 409 of, 20 crystallinity, 397 Niethammer, T., 128,171,194,197, 204, departure from equatorial circularity, 217, 283 409 Nile delta, gravity near, 303, 306 relative density, 412 Niskanen, E., 387, 389, 416 strength, 15, 408, 411 Norgaard, G., 112, 130, 372 stress, 404 “Normal-warp anomalies” of Glennie, temperature, 413 367 Metal columns, illustrating isostasy, 48 North America: Metamorphism, 3 glaciated tract, 326, 329 Mexico, anomaly field of, 370 gravity anomalies, 191, 194 (see also Mid-Atlantic Swell, 257 Canada, Mexico, United States) Miller, A. H., 191, 195, 329, 369 North End Knott Island, Virginia, 76 Millidyne, 106 Norway: Milligal, 106 gravity anomalies, 161, 208, 342, 347 Mindanao Deep, 270, 275, 290, 377, 383 strandflat, 331 Mississippi delta, gravity on and near, Nuotio, U., 130 304, 306 Modulus of rigidity, 2 O Molengraaff, G. A. F., 266 Moment of inertia of the earth, 21, 24, Oahu Island, 298, 379 31, 57 Obi Island, 270 Mont Blanc, orographic reduction of Ocean {see Arctic, Atlantic, Indian, gravity at, 118 Pacific): Monte Rosa, 200 floored by sima, 377 Mont St. Gottard, geoid in section gravimetry on, 252 through, 128, 205 gravity on, 128, 259 Moon: in isostasy, 53 origin, 409, 410 mean density, 17,134 shape, 30, 409 mean depth, 17, 55 triaxiality, 409 Oceanic compartments, 73,136 Moon’s motion and earth’s ellipticity, Oceanite, 19, 20, 375,405,414 30 Oczapowski, B. L., 336 Moore, S., 326, 336 Oldham, R. D., 227,229,245,251,351 Mountain-arcs, 281, 283, 290, 377 Ophiolites, 20 Mountain chains, origin of, 3 Orogeny, 3,15, 398,406, 411 Mountains supported by rigidity of Orographic correction in reduction of earth’s crust, 53 gravity, 118 Mountain stations, 171, 342 Overcompensation, 12, 101, 227, 267 Mount Ouray, Colorado, topographic deflection at, 76 P N Pacific coast-belt, anomaly field of, 163, Nansen, F., 331, 335 189, 191, 193, 369 Nappes of the Alps, 198, 283 Pacific Ocean: Nature’s experiments with icecaps, 309 anomaly field, 262 325 floor, 20 Nero (Mariana) Deep, 291 gravity on, 255, 262 New Caledonia, “ultra-basic” intrusions Western, anomaly field of, 350, 373 of, 20 Pamirs, gravity in, 238, 247 430 Index Pannonian basin, gravity in, 200 “Quasi-orogenic” displacements in Fen- Penck, A., 388 noscandia, 322 Pendulum as gravimeter, 33, 111 Quito, Peru, gravity at, 116 Peneplains, warped, 355, 407 Peridotite, 19 R crystalline, 278, 375 dikes, 20 Radioactivity, 19,61, 282,393, 396, 398, vitreous, 20, 405, 414 409, 411 Permanency of areas of one-sign anom Raman, C. V., 35 aly, degree of, 338, 352, 385 Randsenken, 201, 207 Pesonen, U., 210, 323, 336 Rankine, W. J. M., 5, 6, 34 Petit, F., 38, 64, 82 Rapakivi granite, relation of to gravity, Petrogenesis in relation to earth-shells, 210, 325 3, 18, 399 Recoil of crust, 318 Philippson, A., 212 Recrystallization of rock under load, Pikes Peak, Colorado, 118, 153, 171 317 “Pillars,” supporting positive loads, Red Sea, gravity on, 219, 264 368, 391 Reduction of values of gravity: Plate, loaded, maximum stress-differ Bouguer, 116 ence in, 360 free-air, 114 Plateau basalt, 20 Hayford-Bowie, 121, 140 Plumb line, deflection of, 24, 26, 33, 50, indirect (or Bowie), 126, 128, 183. 65,68,156, 226, 252 259, 348 Point Arena, California, plumb-line isostatic, 120 deflection at, 76 orographic, 117 Poland, gravity in, 200 Putnam, 124 Polymorphic changes, 406 tables for, 141, 160, 348 Positive isostatic anomaly, largest to geoid, 111, 121 known, 212 to station level, 121 Potsdam: Reed, F. R. C., 212 gravity at, 112, 113, 138, 345 Regional compensation (see Compensa system, 138, 149, 196 tion) Pratt, J. H., 30, 36, 38, 40, 42, 64, 82, Regional isostatic reduction 124, 186, 144, 224 257 Pratt type of isostatic compensation, Renquist, H., 335 41, 49, 55, 132 Reusch, H., 331 Pre-Cambrian areas, excessive gravity Rhabdomena stage of Fennoscandian in, 157, 166 history, 311 Precession of the equinoxes, 30 Richter, C. F., 19, 21, 35, 403 Pressure in relation to terrestrial den Riesengebirge, degree of isostasy in. sity, 18 207, 214 Prey, A., 128 Rift belt of East Africa, 218, 222, 250 Prime vertical, 69, 71 degree of isostatic compensation in, Pseudoviscous flow of rock, 9, 384, 390 221 Putnam, G. R., 112, 123, 125, 130, 138, diastrophic conditions in. 223 171, 193, 197 Rigidity, 2, 9 Putnam type of isostatic compensation, modulus, 2 184 of the earth, assumed, 51, 92 Pyrenees, isostatic compensation of, 38, Seismically effective, 2 342, 415 Rings, topographic, 70, 73, 88, 126, 140, 146, 171 Q Roots for isostatic balance, 45, 47, 49, 59, 276, 280, 285 Quarzschweremesser, 112 Rotti Island, 270 Index 431 Rudzki, M. P., 128 Sial (Coni.): Russia, gravity in, 211, 213, 215, 323 origin, 397 thickness, 16, 18, 121, 188, 198, 202, S 208, 221, 259 Siberia, gravity in, 218, 224, 250 Saint Helena Island, 161, 302 Sierra Nevada, root of, 192 Salisbury, R. D., 416 Sills, intrusive, 23 Salonen, E., 202, 217, 283 Sima, 56, 61 Santa Barbara, California, topographic definition, 5, 16, 121 deflection at, 76 density, 121, 208 Sao Miguel Island, 300 “Sinkers” supporting negative loads, Saratov, gravity around, 215 368,391 Sauramo, M , 4, 311, 313, 316, 335, 336 Slope correction in computing gravita Schiotz, O. E., 252, 307 tional attraction, 72, 74 Schleusener, A., 112, 130 Smolen Island, 331 Schmidt ellipsoid, 30 Smoluchowski, M., 277, 308 Schmitz, E., 5 Socla Island, 273 Schwereanliklinal, 200 “Solid” defined, 5, 9 Schweresynklinale, 200 Sorokin, L. W., 253, 307 Schweydar, W., 55, 64, 390 South Africa, kimberlite of, 20 Schwinner, R., 201, 217, 320, 335 Southern hemisphere, need of gravime Sea basins, gravity on, 264, 287, 306 try in, 347 Sea level: Spans: eustatic shifts of, 51, 212, 321, 332 of anomalous areas, 105, 193, 213, figure of earth (see Geoid) 337, 343, 345, 354, 360, 365, 380 mean, 24 of glaciated tracts, 319 Seattle, negative anomaly area near, 395 Spheroid, 24, 25 Sedimentary formations in relation to biaxial, 52 gravity, 17, 50. 157, 223, 228, 252, of reference (standard), 25, 28, 110, 303 138,139, 239 Seismological data, 14, 17, 20, 21, 57, rotational, 25, 32, 51 63, 188, 190, 192, 198, 209, 242, triaxial, 25, 31, 52, 366 257,276,277,291,310 Spitsbergen, degree of isostasy in, 207 Self-welding of sheared rock under Stackier, W., 218, 251 pressure, 402 Sterneck, R. von, 112, 196 Semi-axes of equatorial ellipse, 32 Stifle, H., 283 Serpentine, 20 Stoping, major, 375, 396, 405, 410 Shaler, N. S., 312 “Strain” defined, 4, 5 Shear-energy, 403 Strandflat, 330 Shearing: Strength, 2, 5, 7 localized, in the asthenosphere, 399 fundamental, 5, 9, 10, 13, 340, 355, 403, 406 384 of the crust, horizontal, 399 increased by all-sided pressure, 384 Shearing-stress, 2, 309, 320, 360, 389 of asthenospheric shell, 2, 250, 278 in the mesospheric shell, 411 of crust (lithosphere), 86, 250, 280, Shield areas: 328 gravity in, 250 of earth in earlier periods, 15 isostatic adjustment for erosion of, of earth’s core, 1, 13 402 of earth-shells, 4, 24, 104, 194, 214, Sial, 56, 61 238, 252, 306, 353, 364 definition, 5, 16,121 of materials, 6, 236 density, 17, 121 of mesospheric shell, 2, 15, 408, 411 discontinuities in, 17 “practical,” 9, 10, 13 distribution, 20, 415 ultimate, 8, 9, 384 432 Index Stress, 5, 6 Teddington, England, absolute gravity axes of, 6 at, 113 caused by harmonic loads, 354, 356, Temperature: 357 earth’s internal, 3, 15, 19, 412 compressive, 6 gradient, 60 in asthenosphere, 389 Templates, 74, 145 in beams, under load, 360 Tethyan geosyncline and sea of trans in lithosphere, 13 gression, 244 in loaded plate, 396 Thermal attenuation, 37 in mesospheric shell, 404 Thermal changes of volume, 62, 268 intensity, 6 Thermal gradients, 399, 414 principal, 5, 6 Thomson, W. (Lord Kelvin), 5 shearing, 6 Thrusts, orogenic, 200, 399 tensile, 6 Thyssen, S. von, 112 Stress-difference, 356, 358 Tide-gage data, 313, 326 defined, 5, 7 Tilting of lithosphere in Great Lakes in earth’s body, 4, 102, 157, 341, 381, region, 326 388 Timor Island, 270 in relation to strength, 7 Timoshenko, S., 388, 416 Strips, negative: Tisserand, F., 144 in East Indies, 269, 271, 272, 278, 288 Tonga Deep: in relation to ocean Deeps, 275 gravity on, 254, 291, 347, 377 in West Indies, 286, 287 strength of lithosphere under, 379 Sub-Himalayas, 227 Tonga Plateau, gravity on, 255 Submarine, measurement of gravity in, Topographic deflection (see Deflection 115, 306 of the plumb line) Subsidence of the sial, 202, 212, 374 Topography: Substratum, 15, 19, 267, 374, 400 effect on computed gravity, 140, 144 Suess, E., 376 in relation to gravity anomaly, 151 Sunda Sea, 266 Transverse wave, 21, 400 Superelevation in glaciated tracts, 322 Triangulation, 67, 104, 177, 252, 345 328 Triaxiality of earth’s figure, 25, 404 Survey of India, 4, 5, 29, 140, 224, 342 tests of, 346 392 Troughs, gravity, 226, 229, 234, 241, Survey of India spheroid II, 32, 230, 299, 367, 391 238, 365 Turin, 200 Sweden, gravity in, 347 Turkestan, gravity in, 161, 218, 247, Swick, C. H., 114 250,347 Switzerland: Tuscarora Deep, gravity on, 293 anomalies of gravity, 162, 197 Tyrrhenian Sea, gravity on, 200, 264, degree of isostasy, 158 373 geodetic work, 197 geoid, 127, 205 U mountain root of, 198, 201, 204 regional compensation, 198 “Ultra-basic” rock (layer), 18, 20, 375, 396 T Umbgrove, J. H. F., 267, 279, 284, 374, 376 Tait, P. G., 5 Undercompensation, 12, 101, 227 Talaud Island, 270, 278 Undercooling of asthenospheric mate Tanimber Island, 270, 278 rial, temporary, 407 Tauern granite, 202 United States: Taurus Mountains, 213 anomalies of gravity, 150, 162, 163, Taylor, F. B., 327, 336 182 Index 433 United States (Cont.): Vening Meinesz, F. A. (Cont.): areas of one-sign anomaly, 162, 189, discussions regarding: 191,362 attenuation by radioactive heating, average elevation, 101 268, 282 deflection residuals, 92 compensating roots, 276 degree of isostasy, 82, 99, 102, 158, continental drift, 280 175 convection currents, 278, 373 depth of isostatic compensation, 96, crustal shortening, 278 103 degree of isostasy for deltas, 304 geoid, 78 degree of isostasy for volcanic mean anomalies, 151, 159, 161, 173, islands, 298 183, 188, 224, 344, 349 degree of isostasy for whole earth, uncompensated loads, 102, 104, 156, 120 179, 187, 380 direction of crustal movement in United States Coast and Geodetic Sur East Indies. 284 vey, 4, 34, 48, 66, 112, 119, 121, fields of positive anomaly, 279 127, 131, 159, 174, 182, 205, 304, gravity profiles offshore, 294 329, 363 “Himalayan” geosyncline, 280 United States Lake Survey, 327 origin of negative “strips,” 267 United States Naval Observatory, 305 orogeny, 279, 280, 284 United States Navy, 257, 266 principle of isostasy, 262, 340 United States Standard Datum, 68, relation of earthquakes to “strips,” 79 276 Up warping: relation of volcanism to “strips,” of Cyprus, 212 281 of glaciated tracts, 318, 327, 335, 386 in favor of regional compensation, 259 of middle India, 243 publications, 256, 307 of peneplains, 407 regional reduction, 125, 300 Ural Mountains, gravity in, 215 strength of asthenospherc implied by, Utah, thickness of lithosphere under, 374 394 Venkateswaran, C. S., 35 Verronet, A., 30 V Vertical (see Plumb line and Deflection of the plumb line): Vening Meinesz, F. A., 4, 107, 252, 256, relation of geoid to, 83 278, 348, 349, 389, 416 Vienna system of computing gravity, anomalies found over: 138, 149, 150 Atlantic basin, 257, 260 Viipuri, gravity near, 210 Indian Ocean, 257, 260 Vindhyan sediments, thickness of, 246 mediterranean basins, 257, 264, 373 Viscosity, 13, 59, 84, 213, 311, 389, 397, near deltas, 303 404, 405 near volcanic islands, 298 Visser, S. W., 276, 307 ocean Deeps, 257 Vitreous state, 10, 18, 19, 61, 375, 394, Pacific Ocean, 257, 260 410 “strips” of negative character, 269, Vogt, J. H. L., 333 285 “Void,” 36, 38, 415 buckling hypothesis, 246, 275, 278, Volcanic islands: 282 degree of stability, 303 compares Alps and negative “strips,” gravity anomalies near, 298, 379 283 gravity on, 302, 306 cruises, 256, 261 Volcanism in relation to gravity, 52, crust-warping hypothesis, 229,'399 249, 281, 352 development of gravimeter, 112 Vosges Mountains, uncompensated load discoveries, 256 in, 201 434 Index w Willis, B.. 407, 417 Witting, R., 215, 314, 335 Waldo geodetic station, 68 Woodward, R. S., 411 Walker, J. T., 64 Woollard, G. P., 352 Warping of lithosphere (see Upwarping): World Catalogue, 129, 197, 207, 224 contemporary, 315, 327, 368 238, 249, 264, 348, 372 Washington, D. C., base station at, 138, Wright, F. E., 107 151, 159, 183 Wyoming, gravity anomalies in, 363 Washington, H. S., 13, 122, 355, 415 Waterschoot van der Gracht, W., 267 Y Wave-lengths of anomalous belts, 105, 193, 250 Yap Deep, 291, 293, 377 Waves, seismic (see Longitudinal wave Yield point, 8 and Transverse wave) Yoldia Sea stage of Fennoscandian his Wave-velocity, 20 tory, 316 Wayland, E., 223 Z Wegener, A., 223, 280, 319 West Indian “strip,” 285, 287 Zenith defined, 68 West Indies, gravity in, 289 Zisman, W. A., 5 White, D., 166, 194, 351, 352 Zonal harmonics, 355 Whittlesey beach, 327 Zones (rings) of topography, 70. 73, 88, Whittlesey hinge-line, 390 126, 140, 146, 258